Robot agility is the intelligent integration of (1) high dexterity (orthogonal axes of motion x ranges of motion), (2) near-instant responsiveness, and (3) whole-arm control of contact forces.

Aspect Ratio (of robotic links)

Practical robot structures have cylindrical links with aspect ratios (length/diameter) well above 2:1. Imagine a virtual axial cylindrical shell that just envelopes the physical boundaries of a link, including the joint (elbow, wrist, knuckle, knee, etc.) that drives it. The shoulders can be excluded since they are embedded in the bulk of the body or base. The length of the link divided by the diameter of this virtual cylinder is the aspect ratio for that link. The high aspect ratio of a cylindrical link allows the arm to reach in and around obstacles in its environment, including other parts of its own structure, without collision.

A big challenge in robot design is to balance aspect ratio with payload capability, since the length of the link times the load at the end of a link determines the required joint torque capacity at the last stage of the drive, which undermines aspect ratio. In direct-drive motors, where the motor is the joint, the aspect ratio can easily slip below 2:1.


Inherent (>95%) (open-loop) backdrivability is essential for safe robotic-arm operation around people; operating in unstructured environments; for stable control of contact forces; and for exploiting Jacobian-Transpose safely to enable Cartesian control of forces, haptic objects, and direct Cartesian control of trajectories.

Nonbackdrivability has its place when safety and stable control of Cartesian forces are less consequential (e.g. low-force grippers or graspers). Grippers and graspers spend most their time stationary, either open or locked onto a target object and nonbackdrivability allows the motors to be de-energized during these periods.

All mechanisms and robots are forward drivable. Electric current is converted to torque by a motor, that torque is transmitted through a mechanical transmission (or directly) to a driven joint, and the joint drives its associated link that supports either the next link or an end effector.

Backdrivability is not to be confused with mechanism compliance. Indeed, it is essential that mechanism compliance be much higher than the typical stable servo stiffness (gain).

Within the spectrum of forward-drivable mechanisms, some are simply not backdrivable regardless of the magnitude of the backdriven effort. Some mechanisms with worm-drive transmissions have this characteristic.

The remaining mechanisms are nominally backdrivable at some level of externally applied contact force. However, functional backdrivability requires that the parasitic forces due to friction and inertia be exceedingly small. Impediments to backdrivability are parasitic friction and inertia:

1.      Coulomb (aka dry) friction, the most essential factor, is generated by the sum of all Coulomb-friction contributions from the motor to the joint. Note that the friction contributed by the motor is amplified by a factor of N, where N is the transmission-speed-reduction ratio. Backdrivability (resulting from Coulomb friction) is reported as (Fm-Fc)/Fm, where Fm is the maximum forward-driven output force and Fc is the backdriven Coulomb-friction level.

2.      Damping friction, summed the same as dry friction, is usually not significant at human-scale joint velocities and generally neglected. As with dry friction, damping friction at the motor is amplified by a factor of N.

3.      Inertia is the sum of inertia contributions. However the inertia contribution from the motor rotor, also called “reflected inertia” is N^2. At typical robot reduction ratios 40>N>200, the motor perceived rotor inertia is often much greater than the mass of a human hand and forearm. A haptic device is designed with minimal backdriven inertia by leveraging lightweight (but stiff) materials, N<40, and low-inertia rotor designs, have total backdriven inertias that are smaller than a human’s hand-and-forearm inertia. Low inertia has the added benefit of enhancing safety in the case of unintended collisions.

Backdrivable Robot

A functionally backdrivable robot has 95% backdrivability and less-than-human-hand-and-forearm apparent mass (inertia) when backdriven.


Bandwidth of a robotic arm should be measured by attaching it to a firm base and commanding the horizontally outstretched arm to follow a sinusoidal position command with a fixed amplitude of 10 degrees beginning at near-zero Hertz and then slowly ramping up to build the amplitude curve of a Bode plot. Initially, the measured output will match the input command. However, as the frequency increases the output will not keep up, resulting in reduced amplitude (and phase delay). The frequency at which the amplitude drops by 3 decibels (roughly 30% attenuation) defines the bandwidth in Hertz.

An alternate technique one can use with under-damped robotic arms is to tap the arm and observe its natural frequency with an accelerometer, video camera and frame-by-frame replay (1/30 th second per frame), or the motor encoders themselves if the system is backdrivable.


Backlash is a mechanism phenomenon where small displacements can occur at one end of a mechanism without corresponding motion at the other. Backlash becomes an especially bad problem in closed-loop systems because the pure time-delays (as opposed to less-damaging phase-delays), although small, become significant relative to typical high-bandwidth control leading quickly to poor performance, mechanism damage, and instabilities. In nonlinear control theory, backlash and dry, Coulomb friction are the worst possible parasitic control phenomena because their describing functions are literally undefined (vertical) in the zero-ith order.

As bad as mechanism backlash is in most machines, it is the absolute worst in robots where the inherently complex kinematic transformations from joint to task space cause joints to reverse velocity frequently, even while the tool end of the robot is executing simple straight-line motions.

Bowl Feeder

A large and sophisticated vibrating machine, placed upstream of a robotic workcell to pre-orient parts so that they can be handled with fixed tooling (e.g. grippers) designed for only one or two orientations. A bowl feeder requires roughly the same floor space as the robot workcell and can cost as much. It is one of the hidden costs of tooling that cannot reconfigure on the fly to adapt automatically to various part orientations. Tool changers or turret changers are often used in conjunction with bowl feeders when there may be more that one ultimate orientations and the robot cell must distinguish and swap tools from a tool rack.

Bus Architecture

In robotics, the notion of providing an addressable communications bus (generally serial) and power along the length of the robot (preferably routed inside the robot). The total number of copper conductors traversing the robot arm is nominally 4 (2 for power and 2 for communications). It is even possible to use only 2 wires (for power) and support the communications wirelessly or by modulating a signal over the power-carrying conductors.

Conventional robots use star (aka home-run) architectures rather than bus architectures, resulting in a virtual explosion in the amount of copper wires required, including the wires for rotor-position sensor(s), thermal sensor, and phase-winding leads for each motor must be routed through the flexing arm, out its base, and across to a large controller cabinet.

Cables (mechanical tension elements)

Mechanical cables that do not creep, are axially stiff, yet flexible to bending in any lateral direction make excellent tension elements. If lateral bending is limited to only 1 direction, then thin steel tape is an excellent alternate to cables. However, bending in multiple directions is essential in any robot shoulder or wrist with differential mechanisms. The best material is very-finely stranded stainless-steel cable which allows the tightest bend radius without inducing micro-yielding in the outer fibres and which have extremely high tensile strength in the axial direction.

Cable Creep

For all practical purposes, steel and stainless-steel cables and tapes do not creep in any metallurgical sense. However, cables can micro-yield when subjected to overload stresses. Micro-yielding may look like creep, but confusing them will lead to poor cable-drive designs.

Cable Drives

Cable drives use drive pinions, driven pulleys, idler pulleys, and stepped (bevel-gear equivalent) pulleys to transmit and transform mechanical power. Cable drives are made stiff and strong by operating at high speed. The best material is uncoated 400-series stainless-steel, made of the finest possible fibers, drawn down through dies with maximum %-area reduction to set extremely high axial yield strength. High-performance cable drives are designed for zero cable scrubbing, so sheathing, for example, should not be used. See high-speed cable drives.

Capstan Equation

The capstan equation is critical to the effective design of tension-element drives and explains why sheathed cables lead to rapid failures and instability. It is derived with integral calculus by considering a short segment of cable stretched under tension across a curved surface with some local radius of curvature. The segment is infinitesimally short and measured by a differential angle of arc, d β, with units in radians. The forces at the ends of the segment are resolved into orthogonal axial and radial components where the radial components create a normal force that, when multiplied by the dimensionless coefficient of friction, μ , sustains an infinitesimal friction equal to the difference in axial tension forces.

The infinitesimal frictions can be summed by integrating across some finite distance between any two points along the cable, such as the point of tangency to the point of termination of a cable to relate the ratio of tensions, T High and T Low, at each end of the cable, resulting in the equation:

                T High / T Low = exp( βμ)

The exponential nature of this equation has profound implications. For example a person can easily hold, stop, and control the descent of 150 million kilograms (or 3 Titanics!) simply by wrapping a cable (of sufficient strength) around a rod (of any diameter) 10 times.

The capstan equation can also be used to help explain why so many cable-drive designs result in utter failure. For example a dexterous robotic Hand that relies on tendons traveling through sheaths in order to traverse the complex motions of the wrist joint is subject to the same inescapable mathematics, where the angle is the total included angle inside the sheath. Constrained sheaths have a preferred path that can change, as the wrist moves, chaotically and nearly instantly into a totally different shape as it jumps from one mode shape to another. If the angle decreases suddenly, the accompanying radical drop in friction can (and usually does) bring on catastrophic instabilities that result in lots of ruptured cables. Conversely, the clutch cable in a car, designed and tested to work reliably for a million cycles, may last only a few hundred cycles if someone accidentally makes a subtle change in the routing while performing unrelated engine work.

CANbus Communications

CANbus is a robust, deterministic, and addressable 2-wire serial-communications protocol that operates up to 1 megabit/sec. It was originally designed by Bosch as a sensor-and-control bus for automobiles, where a communications glitch, for example to an electrically operated steering system, can be life-threatening.

Cartesian Space

Cartesian space is a rectilinear, orthogonal description of three-dimensional space. It consists of three infinitely long straight lines that intersect at a mutual point, the origin. The lines are often associated with right-hand X, Y, and Z axes, and half of each line is designated positive. If X, Y, Z labels are used, then label any two line halves as positive and associate the labels X and Y to these two positive line halves. Then rotate positive X by 90 degrees into positive Y and apply the right-hand rule to identify and label positive Z.

Cobots (Cooperative Robots)

Cobots were originated in the early 1990s by Prof. Edward Colgate and Prof. Michael Peshkin at Northwestern University. The word “cobot” comes from human cooperative robots. Their notion was to make robots that channel a human’s input force in an intelligent manner. In this manner, they enhance safety by having a passive-only system while benefiting from the intelligence and precision of robotic mechanisms. Initially, they introduced rolling platforms with intelligent steering where a person input the locomotion. Then they extended their innovation with steerable joints, where wheels on a spherical surface constrain joint motions.

Computer-Assisted Teach-and-Play

Developed by Karl Leeser and Bill Townsend in the early 1990s (see 1994 SME paper by Leeser & Townsend), this became an important contribution to the field that would become haptics.

Coulomb Friction (aka dry friction)

This type of friction is known in nonlinear controls as a hard nonlinearity. Its describing function is literally undefined at zero velocity. For robotic joints that pass through zero velocity frequently, even while following a simple straight path in Cartesian space with constant velocity, significant Coulomb friction make control of torque practically impossible. To overcome the effects of Coulomb friction on trajectory-only control conventional robots have traditionally used very powerful motors that control velocity with a high gain made possible with collocated velocity sensors. While this method rejects the effects of Coulomb friction while commanding trajectories, it also requires massive motors that are not safe around people, use significant power, and bar the use of Jacobian-Transpose techniques.

Controller (two meanings)

The word controller in the field of motion controls has two meanings:

1.      A motor controller takes sensor feedback of rotor position and performs (brushless-commutation) calculations to determine a set of winding currents for that position that will produce either a desired trajectory or a desired torque (in cases with very low Coulomb friction). Then, in most modern motor controllers, a set of PWM signals is generated that control a set of (typically 6) FETs (through charge pumps) arranged in a double-H bridge (in the 6-FET case).

2.      A high-level motion controller coordinates the motions of one or more axes of a robot. A simple controller may apply a PID filter to a single joint to follow a trapezoidal function (velocity vs. time) with limits on acceleration/deceleration and velocity. More sophisticated controllers may control trajectories and forces in true Cartesian space and may exploit modeled observers, nonlinear functions, and adaptive control techniques.

Some controllers, like Barrett’s Puck controller may serve both controller functions, thus blurring the distinction.

Conventional Robots

Conventional robots typically have significant Coulomb friction at the servomotors, joints and throughout the geared or harmonic-drive transmissions. The friction is rejected through velocity control with high-power motors. Conventional robots are not designed with inherent safety. Instead the integrator or end-user must ensure that no person can every enter the workspace of a live robot.

Coordinate Frame

An orthogonal set of three Cartesian, rectilinear axes labeled X, Y, and Z.

Cylindrical Joint

The series combination of 1 revolute joint and 1 prismatic joint connected by a zero-length link.

Degrees of Freedom (DOF)

Degrees of freedom is shorthand for independent degrees of freedom, which is almost always equal to the number of motors, as long as the motors drive independent axes. For example, the BarrettHand™ BH8-26X series has 8 axes or joints. With intelligent mechanical coupling, these 8 joints can be driven by only 4 motors, but the number of degrees of freedom is truly 4 and not 8.

Generally a six-degree-of-freedom robotic arm can place its tool frame origin at any location within its reach and orient that frame arbitrarily anywhere within its dexterous workspace. However, for a fixed position and orientation of the tool frame the arm pose is fixed.

When there are more degrees of freedom than 6-space, the robot arm kinematics are called redundant. For example, a seven-degree-of-freedom robotic arm such as the WAM™ arm remains free to move even while holding a position and orientation.

Denavitt-Hartenberg (D-H)

Denavitt-Hartenberg is a technique for analyzing the type of serial-link kinematic chains used in robotic manipulators in which each frame is defined relative to its adjacent frame via two length dimensions and two rotations. The scheme is flexible enough to work with both revolute and prismatic joints. An important initial step in the analysis is to affix coordinate frames to each sequential link according to a protocol that is consistent with correct interpretation of the D-H parameters.

Denavitt-Hartenberg (D-H) Parameters

The D-H parameters form an n x 4 matrix of parameters that define the kinematic relationship between coordinate frames that are attached to links in a robot. Knowledge of the D-H parameters allows immediate construction of the transformation matrices. Multiplying the chain of transformation matrices enables the final tool frame to be described relative to the user’s robot-base or room coordinates.

Dexterity (see also semi-dexterity)

Dexterity is best described by the effect on a manipulated target object. It is the degree to which the object can be rotated about any arbitrary axis without being bumped by the robot holding it. Another measure is the ratio of the dexterous workspace volume divided by the reachable workspace volume.  

It is sometimes assumed that the number of degrees of freedom alone indicates the level of dexterity. All other things equal, more degrees of freedom supports higher dexterity. But, what if each degree of freedom had only slight rotational mobility from stop to stop? Here are the important factors:

  • Kinematics with orthogonal, mutually intersection joints connected by zero-link lengths rather than joint-link-joint-link... The best kinematics were identified by Stanford researchers four decades ago as SphericalShoulder-InnerLink-RevoluteElbow-SphericalWrist-OuterLink, with identical inner and outer link lengths. Some fudging is required since (except for gimbals) there is some distance between the wrist center and the grasp center.
  • Minimal wrist-center-to-grasp-center distance. This factor is as important as it is subtle.   It is exasperated by the inclusion of force/torque sensors, tool changers, long wrist rolls, tall hands, etc. (See graphic.)
  • Degrees of freedom. Six is good, seven is excellent.
  • Joint mobility. 180-360 degrees per joint, preferably closer to 360.
  • Long slender links that minimally obstruct their own motions.
  • Compact base that minimally obstructs access to the center of the workspace.
  • Minimal singularities.

Dexterous Workspace


The dexterous workspace is a sub-region of the reachable workspace. For every point in the dexterous workspace, a target grasped object can be rotated about any arbitrary axis (at the boundary of that workspace that rotation becomes infinitesimally small).

Differential Mechanism

This mechanism, which is constructed from bevel gears in its conventional form, but can also be made from tension element for advanced performance, is critical to robotic shoulder and wrists joints because it allows the motors to be separated from the joints. The differential mechanism allows a motor-motor-joint-joint structure, where the motors remain stationary and can be moved back toward the base, in place of motor-joint-motor-joint and motor-joint-joint-motor structures, where the bulk and mass of on motor must be carried on the moving structure.

Direct-Drive Mechanisms and Robots

Since the best mechanical drive transmissions are dynamically transparent, meaning they have zero backlash, zero friction, zero mass, and infinite stiffness. Dynamic transparency is equivalent to eliminating the transmission altogether, employing servomotors that drive each joint directly. But the advantages of a transmission are lost as well; the ability to amplify torque while transmitting torque over a distance (e.g. from the base of the robot to the joint) are both absent in a direct-drive implementations. So the motors at all joints must be large and massive. Since even the outer motors are so heavy, motors toward the base must be extremely large to support their own joint torques plus the extra weight and mass of the outer motors. Since there is no transmission ratio (or speed reduction), the motors burn a great amount of power in I^2*R losses. The load from the robot’s own weight is so high that these devices are either limited to 3 or 4 degrees of freedom and mechanically counterbalanced or they are hung from an overhead ceiling and are limited by gravity from displacing far from straight down.


(Ergonomic Assist Device, see IAD)


Encoders come in two main types: incremental and absolute. The sensor types are usually optical, but may also be magnetic or electrical. In absolute encoders, when power is booted, the encoder knows its absolute location before there is any motion. Incremental encoders rely on A and B pulse trains in quadrature to report relative distances and direction. An optional index pulse on a third track allows the incremental encoder to calibrate and begin reporting absolute position only after the rotor rotates far enough (up to 1 full turn) to locate it.

Ethernet Communications

Ethernet is a high-speed non-deterministic serial communications protocol. There are versions for 2-, 4-, and 8-wire variants and optical physical layers, with bandwidth highest in the 8-wire and optical versions. While the overall bandwidth is generally high (with the common TCP/IP protocol), there is a massive degree of overhead and without deterministic benefits, latency can be significant.

Feather Touch

The ability to backdrive a robotic system with only 5% or less of the system’s maximum rated output force.

Feedback Control

Feedback control, also known as closed-loop control, relies on one or more measurements of the output performance of a system, machine, or robot. Then it compares that measurement to the desired input(s) and uses a control algorithm such as PID to close the loop.

Feedforward Control

Feedforward control is an open-loop control technique that improves performance in precision and responsiveness without any loss of stability. A good example is gravity compensation in a backdrivable, articulated robotic arm. In this case, for a given arm posture and knowledge of the relative gravity vector, a set of joint torques can be easily calculated that offset the effects of gravity on the links. This particular feedforward technique, when combined with PID control, eliminates much of the steady-state error of proportional control due to sagging in gravity and so allows the integral gain to be substantially or completely removed thereby reducing oscillatory behavior and improving the margin of stability.


Software that is stored inside an embedded processor inside a robot component to give it local intelligence that is upgradeable. Local intelligence generally reduces communications demands.

Force Closure

There are two ways to secure a target object: force closure and form closure. Friction force is equal to the product of the coefficient of friction times the applied normal force. Grippers without specially-shaped custom gripper jaws rely on force closure to secure a target object by creating high normal forces to generate high enough friction forces to prevent the target object from slipping.

Form Closure

There are two ways to secure a target object: force closure and form closure. Form closure does not rely on friction force and so can handle target objects with delicacy without compromising security.

Forward Kinematics

A unique function can be derived for the kinematic structure of any robotic manipulator that gives the universal Cartesian coordinates of a given frame (usually the Tool Frame) of the robot based on an instantaneous knowledge of joint positions and the kinematic structure.


A local X-Y-Z Cartesian coordinate frame is attached to each link as an essential step in preparation for mathematical kinematic analysis, such as Denavitt-Hartenberg.

GCL (Grasper Control Language)

GCL is a general, extendable, and open protocol for commanding the actions of multi-fingered graspers across serial communications lines (Ethernet, USB, IEEE 1394 firewire, CANbus, RS485, RS232, etc.). The protocol was developed through collaboration between engineers at Barrett Technology and the Massachusetts Institute of Technology. GCL has two modes:

Supervisory mode enables high-level commands to be sent to a Grasper that are parsed by a supervisory processor embedded inside the Grasper so that high-level commands (e.g. close fingers 1 and 3). In this mode, a person can control the Hand from a terminal.

RealTime mode uses the full bandwidth available to allow realtime low-level control by the user on the user’s own computer, independent of the embedded processor on the Hand. Sensors values designated by the user are fed back at realtime while commands issued by the user’s computer are sent in realtime.

Graceful Robot Motions

Graceful robot motions refer to robot motions supported by high enough dexterity, redundant kinematics, and smooth trajectories that the entire robot takes on a sense of grace of a ballet dancer.


A grasper is a dexterous (or semi-dexterous) robotic Hand whose primary mission is to secure target objects by wrapping digits around an object that is secured through form closure without the need for high forces, adjusting to variations in shape, size, and orientation on the fly within a few-hundred milliseconds. A grasper is designed to replace tool changers, tool racks, multiple custom-designed grippers.

Grasper Control Language (GCL)

See GCL.


GraspIt is a generalized computer program developed by Prof. Peter Allen and Dr. Andrew Miller at Columbia University that directs high-level grasping of articulated multi-fingered robotic Hands independent of manufacturer or model. It is one of the most comprehensive programs of its kind, and (as of the publishing of this glossary) has been made available to the research public.

Gravity Compensation

Gravity compensation is a specialized type of feedforward control used in backdrivable robotic arms. The kinematics, relative orientation of the gravity vector, and instantaneous pose must be known or knowable. The link and payload masses must be known a priori or measured (in a process called identification). In these circumstances, only a few sines and cosines must be evaluated to determine the unique set of joint torques required to balance gravity precisely and these balancing torque change only gradually as the arm moves or is pushed around the workspace.


Grippers are simple robotic Hands that rely either on friction to secure (small) parts (<50 grams) or custom (soft-jaw) gripper shapes pre-conformed to each part of a given size, shape, and orientation. Grippers come in 4 types, parallel-sliding versus pivot-jaws and 2 fingers versus 3. To handle different parts or the same part in different orientations, several grippers are used, each with its own customized jaw sets. Tool changers (or turret changers) are added to the end of the robot tool racks placed at the edge of the workspace. The arms in this case tend to be larger to maintain workspace after the tool rack is installed. Also, upstream part orientation stations, such as bowl feeders, are often used to limit the number of possible part orientations.

Compared to using a programmable grasper, the hidden costs of grippers include:

  • Requirement for additional workcells to handle different parts.
  • Additional specialized equipment, such as bowl feeders for part pre-orienting, which can nearly double the workcell footprint.
  • Requirement to keep tool spares in a tool crib incase of robot crashes.
  • The dexterous workspace is reduced dramatically as the small distance between the kinematic wrist center and the grip center is increased with the addition of the tool changer.
  • Requirement for a larger robot payload capability to carry the extra tool-changer mass and need for faster speeds to maintain cycle times. Larger robot arms cost more, require larger footprints, respond slower, and elevate the threat to human safety.
  • Requirement for a larger robot reach to accommodate the dexterous workspace reserved for the tool rack.

Haptic Device

An articulated machine designed to come in physical contact with people, usually through a handle that a person grasps, and to have the capability to control, the forces that the person experiences.

Haptic Object

A haptic object is a virtual object that is suspended (and can move and morph) within the workspace of a haptic device. A person moving the handle, stylus, or thimble of the device senses resistance forces generated by the device to simulate collision with the membrane of the haptic object.


See also Kinesthesis and Psychophysics. Except for sensing heat transfer, the perception of touch is generated both by kineasthetics and tactile sensors in the human body. Haptics is the study of the perception of touch in exploring and controlling objects and fluids that we can touch.

Hard Nonlinearities

However, it Hard nonlinearities exist when either it input-output description or one of the descriptions mathematical derivatives is discontinuous (i.e. includes a vertical slope). The badness of a hard nonlinearity can be ranked by the number of derivatives required to generate the vertical slope. The absolute worst hard nonlinearities have vertical slopes in the fundamental description.  

Harmonic Drives

A harmonic drive is a compact high-reduction gear reducer. The gear teeth are mounted on the exterior of a flexible cylindrical cylinder with a tooth count different by only 1-5 teeth from the mating internal gear. Harmonic drives are very important in industrial robots with most joints driven by them. However, they suffer from limited backdrivability (far below 95%) and gear noise.

 “High-Speed” Cable Drives

High-speed cable drives are orders of magnitude stiffer and stronger than conventional cable drives.

IAD (Intelligent Assist Device)

According to the RIA T-15 Committee of Safety Standards for IADs, “a single or multiple axis device that employs a hybrid programmable computer-human control system to provide human strength amplification, guiding surfaces or both.”

Image-Guided Surgery

Image-Guided Surgery combines advanced imaging techniques, realtime position trackers, image-data manipulation, and 3-D displays to help doctors plan and guide surgical operations with better precision. In the 1990s, the first wave of position trackers and 3-D displays were solely visual, but telerobotic and haptic robotics are beginning to augment or replace the position tracking and visual 3-D displays.

Inherent Safety

Just as with the hammer that falls from an overhead shelf or the hapless person whose chest falls on a pencil protruding from a lawn, virtually no tool is inherently safe. In the past, robots were truly dangerous, and so cages were mandated by industrial guidelines, such as those published by ANSI/RIA, to segregate robots from people.   Workers defeating these barriers led to several documented deaths, generally caused by slow crushing. Unfortunately, the compulsory barriers relaxed any incentive to design robots with inherent safety that might someday enable hand-in-hand collaboration with people.

Of course, robots in cages cannot, by definition, collaborate with people, assist people, or become mobile.

Backdrivable systems, however, have become safe enough, that the remaining danger is far outweighed by the benefits to society, for example in improved surgical outcomes.

Inherently Dangerous Haptics (story of noncollocation)

Sensor collocation is critical to ensure dynamic system stability in feedback systems.   The lack of collocation, meaning the introduction of significant (slow) dynamics (usually from the controlled machine itself) between an actuator and the sensor compromises stability and, in the case of Haptics, human safety. A prime example is the use of force/torque sensors located at the endtip of a robotic device in an attempt to make the robot appear backdrivable. While such force/torque sensors perform with high precision and high responsiveness (>1,000Hz), the robot arm dynamics are substantially slower (<20Hz), even in the lightest, stiffest robot arms in existence. There are several patches that can regain a stable system, but each patch compromises performance.

Input Shaping

This is a sophisticated form of feedforward command that considers multiple vibration modes of the system under control and uses a convolution to generate a control signal that gives optimal performance without oscillatory effects. Neil Singer earned his doctorate at MIT in 1990 by introducing the most dramatic contributions in this field.   He since founded Convolve, Inc. of New York, and Convolve’s algorithms are leveraged in most hard drives in service today.

Inverse (of a Matrix)

Only square matrices can be inverted, an operation that (especially in robotics) is computationally slow and so must be done offline in practical applications.Small errors blow up near mathematical singularities, and there are many singularities in a robot’s workspace.

Inverse Kinematics

The object of inverse kinematics for a particular robotic manipulator is to calculate a set of robot joint positions based on a desired set of Cartesian coordinates of the tool frame. 


The Jacobian is a mathematical matrix representing the first derivative of kinematics and very important in robotics.There are two interpretations of the Jacobian. The second is only used in advanced robotics and is more powerful:

1.      Given a tool frame velocity described in joint space, it allows quick calculation of the same velocities described in Cartesian space. However, (conventional) robots need the reverse calculation in order to generate true Cartesian paths (e.g. in paint spraying, seam welding, laser cutting, adhesive dispensing, etc.) which can be done (in special circumstances) via a 2nd (and slow) calculation known as the Jacobian-Inverse. Since this calculation is slow, it cannot be calculated in realtime, so must be done off-line.

2.      The Jacobian can also be used to translate forces and torques described in Cartesian space, the other way around without any matrix inversion, to Joint space. However, this information is only available in advanced robots with intrinsically high (>95%) mechanism backdrivability. Non-backdrivable mechanisms sometimes are retrofitted with joint or end-point force-torque sensors, but these techniques compromise safety and are not recommended.


Jacobian-Inverse is a computationally slow and burdensome operation in robotics, virtually barring true realtime Cartesian control. It is a matrix inversion in the formal sense, which means that it must be well conditioned (the robot must be far from singularities) and it must be square (so only non-redundant robots can have a Jacobian-Inverse).

Conventional, nonbackdrivable robots that must follow paths prescribed in the global Cartesian coordinates of the room (e.g. paint-spraying, drilling, cutting, welding, dispensing) require calculation of the Jacobian-Inverse which is generally calculated off-line on a powerful processor.


Unlike Jacobian-Inverse, Jacobian-Transpose requires absolutely zero computation to derive it from the Jacobian. A mathematical matrix transpose affects only the order in which the matrix elements are written into and subsequently read from memory.

In advanced backdrivable robots, the Jacobian-Transpose is a mathematical silver bullet that enables full Cartesian control of both forces/torques and trajectories in realtime by eliminating the need to calculate either the Jacobian-Inverse or the Inverse Kinematics. Although this technique has been known for decades, the lack of highly-backdrivable mechanisms relegated it initially to the trashbin of unusable theory until the technology underlying the WAM™ arm was developed.

Joint (mention revolute, prismatic, spherical)

A robot joint is a bearing-based mechanism that constrains the relative motion of two adjacent links. Robotic joints are either revolute joints or prismatic joints. Prismatic and revolute joints can be combined in series to create spherical and cylindrical joints.


Kinematics is the modeling and formalized mathematical analysis (including forward and inverse kinematics and Jacobians) of the motions (angular and rotational positions, velocities, and accelerations) of articulated mechanisms that are made up of a combination of revolute or prismatic joints separated by rigid links. The analysis begins by affixing local Cartesian x-y-z coordinate frames to each link (even those of zero length). In robotics, frames are generally attached according to the highly structured Denavitt-Hartenberg (DH) method in which only 4 parameters (the DH parameters) are required to define the location of one frame relative to an adjacent frame. Kinematics is central to the ability to control the complex motions of a robotic manipulator. It can also be used in relating joint forces and torques to globally applied forces and torques.


Link in robotics has a formal and a less formal definition. The formal mathematical definition of link is the solid body that separates and fixes the relative locations of a pair of joints. This definition is useful in the formulation of the kinematics mathematical description of a robot. It is also common for the links in shoulders and wrists to have zero length. For example, to a kinematician, a 7-degree-of-freedom human arm is made up of 7 one-degree-of-freedom joints separated by 6 links. The first and last two links have zero length. Only the third and fourth links, upper arm and forearm, have non-zero lengths.

Less formally the same arm might be considered a 2-link arm (upper arm and forearm), with a spherical shoulder joint, a revolute elbow, and a spherical wrist joint.


In robotics, the ability to control the position, orientation, or form of target objects.  


In robotics, manipulators generally refer to a mechanism having at least one serial chain of links. There may be several serial chains in parallel as with a human hand or a single chain as with a human arm.


Metrology is the science and technology of measuring surface geometries with high precision.


Micro-yielding, often mistakenly and misleadingly called cable creep, occurs when instantaneous cable tension loads combined with bending-induced (tension) stresses in the outmost cable fibers exceed the yield strength in the material. The signs of advanced micro-yielding can be detected by a prickly texture to the back of the cable (counter-intuitively facing away from the pinion surface). Micro-yielding is controlled in a backdrivable robot simply by limiting the maximum motor torque.

Minimally-Invasive Surgery

The minimization of the size and number of incisions during surgery. Large incisions increase trauma to a patient’s condition, lengthen the recovery period, and increase the probability of a second subsequent surgery to remove excess scar tissue. Minimally-invasive surgery, however, often blocks the surgeon from easy access, limiting both the ability to see directly what is going on and hampering the use of instruments. Computer-enhanced image guidance has made some of these surgeries feasible, and the advent of robot-assisted surgery is beginning to overcome many of the instrument issues.

Noncollocation F/T-Sensor Instabilities

Noncollocation exists in closed-loop feedback control systems when the source of an action (like a motor) and a sensor upon which the action is controlled are separated by significant (i.e. slow) dynamics. Designers of robotic systems often forget that a closed-loop system like a robot is only as fast as its slowest part, the mechanical system. To improve overall poor bandwidth, designers often increase sensor speed or bandwidth from the electronic controller that generates the control signal even though the mechanical structure is far slower. The bottom line is that increasing the speed of the electrical and computational subsystems above a few hundred Hertz is usually meaningless compared to improving the main robot dynamics, which generally limit robots to just a few hertz of bandwidth.

Indeed, in a closed-loop feedback system, trying to apply a control law well above a few Hertz based on a noncollocated sensor (most commonly a force or torque sensor) leads to dangerous dynamic instabilities.


(See also Hard Nonlinearities)  Nonlinearities create a tough challenge for the control of any machine, whether controlled open loop (whether by a person or a computer processor) or with closed-loop feedback control with sensor feedback. While the key components used in today’s solid-state controller systems have been designed for linear performance, key nonlinearities, namely friction and backlash are inherent in the world of mechanisms.  


The geometric interpretation of orthogonal is the notion of right angles, perpendicularity, or to entities oriented 90-degrees apart. But orthogonal also conveys the specific notion that actions in orthogonal directions are independent of each other. Familiar orthogonal spatial coordinate systems include Cartesian, cylindrical, and spherical.   Orthogonality also becomes important in the higher-order spaces used frequently in robotics, where geometric interpretations lose meaning.

PhanTom Haptic Device

The PhanTom, originally called the mini-WAM™, was the first commercially successful haptic device and debuted in the early 1990s. The device was designed by Thomas Masse and his MIT advisor, J. Kenneth Salisbury. The two were cofounders of SensAble Technologies.

PID Control (Proportional-Integral-Derivative)

Introduced 1922 for the active control to hold guns steady in the inertial frame during pitching and rolling in heavy seas, PID control is the simplest style of automatic control. It is the simple sum of three components of control: proportional, integral, and derivative. It should be noted that any one or pair of these components of control can, and often are, used independently and in all possible pairs. For example, the integral component can drive systems unstable, and so may be set to zero when stability trumps accuracy.

In PID control, a sensor measures a scalar aspect of performance of a system or machine (e.g. actual position along a linear track) and subtracts that value in realtime from a commanded control signal (desired position along the linear track) to generate an error signal. The proportional control signal then becomes the product of the control error times a (usually preset, proportional) gain (a number) that balances stability and precision. Higher gains reduce error while decreasing stability.  

The derivative and integral components both rely on the history of the error signal.   In the case of integral, the error is literally integrated mathematically over time and multiplied by its own (integral) gain (number). With integral control, the longer an error persists the stronger the correction command becomes until, the control effort saturates, the machine breaks, or (as desired) the error is overcome. While integral control is important for eliminating persistent error, it also tends to make otherwise-stable systems unstable or at least more oscillatory.  

Derivative control literally takes the mathematical derivative (or rate of change) of the error and multiplies the result by its own (derivative) gain (number). The resultant control signal behaves like fluid damping or wind friction, where a resisting force is proportional to speed, or, in this case, the rate of change with respect to time of the error. In other words, derivative control damps down fast changes. Opposite to integral control, derivative control tends to stabilize an otherwise unstable system. An odd and counterintuitive quirk of derivative control is that any high frequency noise in the sensor (or command) signal can create enormous derivatives, even when the noise amplitudes are barely measurable. When multiplied by the derivative gain, the result can be terrible vibration that can easily be confused with the oscillatory nature of integral control.

Prismatic Joint

A joint that allows only 1 degree of freedom of motion that is described by a pure length displacement. The name comes from the notion of an extrusion with a prism cross-section as one rigid body (link1) along which a second rigid body (link2) with an exactly matching prismatic cross-section cut through it slides. The prismatic shape, unlike a simple rod and round hole, prevents rotation between the two bodies. An example would be an extension ladder.


Psychophysics studies the relationship between physical contact and the brain. Ernst Weber laid the groundwork for psychophysics and experimental psychology; and his student, Gustav Fechner, developed psychophysics into a science by student in the mid-19 th century with the notion of “just noticeable difference” in physical stimuli.   Today psychophysics is developing understanding about the relationship of physical and visual exploration.


An ultra-miniature brushless servo controller fit into an ultra-high-precision encoder.   Developed over several years by Barrett Technology, this puck weighs only 44gms and is only 35mm (dia) x 17 (high) with connectors.


A square wave has two states (call them low and high) over each cycle relative to the x axis. Whether one slides along the x axis in the positive, negative direction, or even reverses directions, the pulse sequence is always the same (…high-low-high-low-high-low…). Two square waves, locked ¼-cycle out of phase, generate four 4 (quadrature) unique states which we can label (w, x, y, z) as follows:
w = high-high
x = high-low
y = low-low
z = low-high

Sliding in the positive x direction generates w-x-y-z-w-x-y-z-w-x…
Sliding in the negative x direction generates w-z-y-x-w-z-y-x… 
Sliding positive and reversing at the bolded x generates w-x-y-z-w-x-w-z-y

Incremental encoders exploit quadrature to track position changes, even when the sliding direction might change, as it does in servos.


Realtime exists when the bandwidth of the controller and sensors is guaranteed always to exceed the electromechanical bandwidth of the robot being controlled.

RealTime Mode

See also GCL (Grasper Control Language).   RealTime is one of the two GCL modes.   RealTime mode exploits the full communications bandwidth available, allowing the user’s processor to close control loops outside the controlled grasper. The user’s program can vary on the fly, or the user can predetermine, packet lengths, enabling the user or user’s processor, to trade the number of sensor reports per packet with round-trip time delay.

Redundant Kinematics

A non-redundant robotic arm required to be able to reach a point in 3-space requires only 3 independent joints. A redundant arm requires 4 or more joints.

A non-redundant robotic arm required to be able to reach a point in 3-space and any orientation at that point requires 6 independent joints. A redundant arm requires 7 or more joints.


Rehabilitation is essential to recovery from various traumas, such as a stroke or broken leg. As the population ages, it is likely that the frequency of these traumas will increase along with the rehabilitation effort. In the past rehabilitation was implemented by a physical therapist or an occupational therapist that would teach the patient various physical exercises. The intensity of rehabilitation often affects the ultimate level of recovered function for the patient. Robots in rehabilitation do not tire, maintain precision in both trajectories and forces/torques, can follow special realtime control laws that human therapists cannot. Also robotic rehabilitation opens the door for massive data collection on trajectories, forces, and torques, to help judge whether a specific therapy should be continued or changed.

Revolute Joint

A one-degree-of-freedom joint that is described by a pure angular displacement with no translational component. An example is the human elbow.

Rotor Position Measurement

There are two reasons to measure a motor’s rotor position:

  • To enable electronic commutation
  • To measure arm position


Grippers capable only of holding a pre-determined object are not dexterous, while human hands that can manipulate objects freely are fully dexterous. Graspers, which are designed to secure target objects of a wide range of shapes, sizes, and orientations, are considered either semidexterous Hands or dexterous graspers because they grasp and secure target objects with dexterity but have limited capability to manipulate objects

Serial Communications

Serial Communications has come a long way from RS232, the first major standard.   But better alternatives are quickly replacing it. These serial-communications alternatives include Ethernet, USB, FireWire (IEEE 1394), and CANbus.

Serial Port

Refers to the slowest of serial commications protocols. A legacy port, still available on most PCs to support RS232 (usually ASCII) serial communications to perpherials. Serial communications are slower than other modern high-speed serial communications, but are still ubiquitous.


In scalar mathematics, dividing by zero generates a singularity, causing functions to blow up towards infinity. In the matrix mathematics that describe and help control robotic manipulators there is a analogous concept where a determinate equals zero.

Space-Vector Commutation

Space-vector is the most advanced method of creating commutation torques, even surpassing the performance of “sinusoidal” commutation. When combined with high encoder resolution, this form of commutation gives the highest possible motor efficiency and smoothest output torque. Barrett’s Puck controller electronics are streamlined to support space-vector commutation.

Speed Reducer

To maintain practical link aspect ratios, joint drives must be compact. The magnetic coupling torque, even using the strongest possible magnet material is 1 to 2 orders of magnitude too weak. A simple solution is to employ a speed reducer (based on gears, harmonic drives, cables, etc.) which trades wasted top-end speed for torque. It is interesting to note that a speed reducer (or torque amplifier) is a transformer, similar to electrical transformer.  

Spherical Joint

A spherical joint is the series combination of 3 revolute joints connected by two zero-length links. Examples include the human shoulder and human wrist.

Steriotactic (aka Steriotaxic)

Steriotactic is a term originally introduced in the context of neurological surgery and means the full control of the location of a surgical tool, electrode, or hypodermic needle relative to a patient’s vital anatomy, especially regions of the brain.


Stiffness in robotics has the same meaning as the stiffness of a spring; and high stiffness is always beneficial, even in backdriven robots. If you begin to pull on a coil spring, the rate of change of the pull force relative to the spring deflection can be measured and plotted. The slope of the curve with units of force/distance is the stiffness of the spring. Similarly, if the spring is torsional, then a torque is applied and the rotation measured and plotted producing a stiffness with the units, in this case, of force x distance. In robotics high stiffness is always better. So, in a robot stiffness can be measured at the endtip of the arm with the arm outstretched. Since robot deflections can be viewed either as angular displacements of (revolute) joints or as a Cartesian displacement. Either set of units can be reported, related directly by the square of the reach (distance) of the arm.

Supervisory Mode

See also GCL (Grasper Control Language). Supervisory mode enables high-level commands to be sent to a robotic Hand that are parsed by a supervisory processor embedded inside the Hand to enable local high-level commands (e.g. close fingers 1 and 3). Supervisory Mode requires very little or no bandwidth or user-processor power to execute complex actions.

Teach-and-Play Programming

Sometimes called lead-through programming, teach-and-play programming is done on a 95%-backdrivable arm with layered safety protections and gravity compensation active. The user applies (literally) a feather touch to move the arm to different positions. This technique is especially useful in programming arms with redundant kinematics because the user can easily direct the end of the arm with one hand and the redundancy with the other hand, avoiding obstacles and keep-out zones along the way. There are two methods for recording the motions:

1.      Discrete points where the user chooses the location of each key point.

2.      Continuous points captured at a predetermined rate (e.g. 100 Hz)

Also, there are three methods for interpreting and playing back the points:

1.      Play back the discrete point through the default trajectory generator where the user can accept or edit defaults such as time of flight between each set of points.

2.      Play back the continuous points without data filtering.

3.      Play back the continuous points after applying curve fitting techniques to ensure optimized motions.

Tension Elements

Tension elements are engineering materials that can support an axial force and are capable of sustaining combined tension+bending stresses around a pinion (smaller of two pulleys) without yielding the outer fibers. Practical examples include, cables (of various materials), bands,

Two of the most successful tension elements are made of work-hardened 400-series stainless-steel. One of the forms is finely-stranded cables for machines and robots that move freely in 3 dimensions. The other is stainless-steel tape for robots (like SCARA robots) that move in a plane.

Tension-Element Drives

Tension-element drives ( cut and paste from old proposals).  

Tool Changer

Used in conventional robotics, a tool changer enables different custom tools, one or more for each subtask within a robot application. They reduce the number of possible part orientations, and therefore the number of bowl feeders are usually employed upstream of the robot workcell to reduce the number of orientations.

Tool-Center Point (TCP)

The tool-center point (TCP) can change for each tool. It is the point about which commanded Cartesian rotations are centered. By default, the TCP is located 1,000 mm from the shoulder center of an outstretched WAM™ arm.

Tool Frame

This is the final coordinate frame in the kinematic description of a robot.

Tool Rack

A tool rack is a precision tool storage bin that holds up to dozens of different custom-designed robot-end tools. The tool rack must hold tool locations precisely so that a tool changer can find them via dead-reckoning, blind without visual servoing. Naturally, the tool rack must be within the dexterous workspace of the robot arm, so when deciding to employ a took rack, a larger arm must be selected. The larger arm size comes with greater reach, inertias, and torques, making ever more imperative to enhance safety barriers. For performance, the increased arm-link inertias will slow cycle time.

Torque Cogging

Periodic variations in brushless-motor torque that are caused by interactions between permanent magnets bonded to a rotor and the slotted iron core in the stator. These variations tend to be repeatable and do not vary significantly with operating conditions, so it is relatively easy to measure and electronically cancel their effect.

Torque Ripple

Periodic variations in sinusoidally (or space-vector) commutated brushless-motor torque. These variations are caused primarily by unbalanced phases as the gains and biases of different current sensors drift differently with operating conditions, such as temperature. Barrett Technology’s patented technology matches the gains and offsets identically, thereby eliminating the primary source of torque ripple.


When the inner link of a BarrettHand™ makes first contact with a target grasp object, the patented TorqueSwitch™ locks the inner link against the target and shunts all available motor torque to the outer link to secure the grasp.


A transformer is a device for shifting the force-speed (mechanical domain) or potential-current (electrical domain). In robotics, transformers are used most frequently to amplify torque from the motor to the joint to maintain a practical link aspect, with a proportional sacrifice of speed. The opposite is never implemented in practice; although, sometimes a compromise is made (see direct-drive) in order to eliminate the transformer altogether.


A transmission has the same meaning in the mechanical and electrical domains and has either one or both of the following two capabilities:

1.   transmitting power over a distance

2.   shifting the mechanical force-speed (or electrical potential-current) relationship (see transformer)


A very stiff mechanical transmission (the analogous holds true for electrical power transmissions) with very little inertia has no significant dynamics at application frequencies. So, even if the power is transferred over a long physical distance, the dynamic model need not include them. It is also assumed that the transmission ratios remain constant and add zero or negligible friction.

Transpose (of a Matrix)

Unlike the mathematical inverse of a matrix, the transpose is available for any matrix, regardless of rank, size, conditioning, or whether square or rectangular. Not a single processor multiply or add is needed to determine the transpose. It requires only reversing the row and column indexes when reading from versus writing to the matrix in memory.

Trajectory Control

The control of positions and/or any position derivatives (velocity, acceleration, jerk) described in either Cartesian or joint space. In haptic applications, the trajectory may be controlled on one or more dimensions while forces and torque are controlled in the remaining dimension(s).

Turret-Style Tool Holder

A turret-style tool holder carries 2-4 tools that can be swapped rapidly (~1-2 seconds) compared to a tool changer (~10-20 seconds), and does not require a tool storage rack. The drawbacks of the turret-style

  • Extra weight of the turret and carrying all tools simultaneously requires a larger robot arm with higher payload capacity. Larger robot arms cost more, require larger footprints, respond slower, and elevate the threat to human safety.
  • Higher inertia of carrying all of the tools all the time slows the robot.
  • As with tool changers, the extra distance between the wrist center and the grip center reduces the dexterous workspace dramatically.
  • Since the unused tools extend laterally at odd angles, the robot’s motions must be carefully programmed to avoid colliding with any part of the turret holder and the turret cannot operate (switch tools) unless it is sufficiently clear of the robot links, obstacles, or the workpiece.
  • Still requires gripper soft-jaw customization (see grippers), including the procurement and tool-crib storage of extra back-up grippers for each style.


Versatility (including easy or automatic reprogramability, agility, dexterity, and intelligent sensor fusion) is the root benefit of a robot. Surprisingly, there were virtually no large commercial deployments or robots that leveraged versatility before this century.

Virtual Reality (VR)

Virtual reality creates sensory stimuli to alter or enhance a person’s perception of the immediate environment. This altered perception most often involves visual and aural sensing, but may be greatly enhanced with haptics which seem not to distract a human’s visual information channels to the brain.

Whole-Arm Manipulation (2 meanings)

There are two meanings to Whole-Arm Manipulation, both exemplified in Barrett’s WAM™ arm:

1.      The inherent capability of a robot to control contact forces with inherent safety and robustness all along its link and joint surfaces, from the base of the arm through its end. This capability is especially enabling when applied to a kinematically redundant arm.

2.      A (w)holistic approach to robot design enhances safety and performance while reducing intrinsic manufacturing, shipping, training, software, footprint, power, and servicing costs. For example, conventional robot designs continue today to depend on legacy drive technologies that introduce friction, backlash, torque fluctuations, or generate poor aspect ratios. Then conventional designers go to great lengths to attempt to mask these effects at the expense of safety or other performance metrics. The (w)holistic approach leverages simple, (high-speed cable) drives that do not introduce these problems in the first place and yet exceed the highest standards of conventional performance.

Workspace (see also Dexterous Workspace)

A robot’s workspace is the reachable volume surrounding a stationary robotic arm, defined by its reach. Depending on the task, much of this workspace may be useless. However, overall workspace is far less important than the dexterous workspace, which is a subset of the overall workspace, if it exists at all.