7. Robot Control Systems

Introduction and Context

A robot is not autonomous merely because it possesses sensors, actuators, and a mechanical structure. Its useful behaviour depends on a control system that converts motion or force objectives into actuator commands while accounting for dynamics, uncertainty, disturbances, computation, and safety. Robot control therefore provides the bridge between a robot’s mechanical design and its intended task.

In earlier analysis of robot kinematics, the relationship between joint variables and end-effector pose was established. Control goes further: it determines how joint torques, velocities, or actuator currents should be generated so that a robot follows a desired trajectory, exerts a specified contact force, or behaves compliantly when interacting with its environment. At postgraduate level, robot control must be viewed as both a mathematical discipline and an engineering activity. A controller that is theoretically stable may still fail because of sampling delay, actuator saturation, inaccurate calibration, friction, communication latency, or unmodelled flexibility.

Robot controllers are commonly designed in joint space or task space. Joint-space control regulates joint positions, velocities, or torques directly. Task-space control regulates quantities such as the position and orientation of an end effector, contact force, or interaction impedance. The choice depends on the task, the available model, sensing arrangements, computational resources, and safety requirements.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Explain the architecture and principal terminology of robot control systems.

2. Formulate joint-space and task-space control problems using kinematic and dynamic models.

3. Design and compare PID, feedforward, computed-torque, force, impedance, adaptive, robust, and model-predictive controllers.

4. Analyse tracking error, stability, robustness, actuator limitations, and real-time implementation constraints.

5. Select an appropriate control strategy for industrial manipulation and human–robot interaction.

6. Diagnose common control failures and recommend engineering improvements.

The Control Problem in a Robotic System

A rigid-link manipulator with n joints is often represented by the dynamic equation

M(q)q̈ + C(q,q̇)q̇ + g(q) + τf(q̇) + τext = τ,

where q is the vector of joint positions, M(q) is the positive-definite inertia matrix, C(q,q̇)q̇ represents Coriolis and centrifugal effects, g(q) is the gravity vector, τf denotes friction and other dissipative effects, τext represents external joint torques, and τ is the actuator torque vector. In practice, the model may also require elastic transmission, motor dynamics, backlash, payload uncertainty, and actuator limits.

The desired trajectory is described by qd(t), q̇d(t), and q̈d(t), or by a desired task-space trajectory xd(t). The tracking error is commonly defined as e = qd − q in joint space. A controller computes a command from the error, its history, the desired motion, measured states, and possibly a model of the robot and its environment.

A complete control loop includes sensors, state estimation, a control algorithm, power electronics, actuators, mechanical transmission, and the physical environment. Feedback is essential because the model is never exact. Feedforward is valuable because feedback alone must create corrective action after an error has appeared. High-performance control combines both.

Important performance measures include steady-state error, rise time, settling time, overshoot, bandwidth, disturbance rejection, energy consumption, interaction force, computational load, and robustness to parameter variation. These measures frequently conflict. Increasing gain may improve tracking but amplify sensor noise and excite structural resonances. A controller must therefore be evaluated as a closed-loop system rather than by gain values alone.

Essential Terminology and Structural Choices

A plant is the physical robot and its actuators. A reference or set point is the desired position, velocity, force, or trajectory. A tracking error is the difference between the reference and measured output. Feedback uses measured output to correct deviations; feedforward predicts the command required from the desired motion or an estimated disturbance.

The control bandwidth is the frequency range over which the system can track commands effectively. The sampling period is the interval between successive digital control computations. Latency is the delay between measurement, computation, and actuation. Actuator saturation occurs when a motor cannot provide the requested torque, velocity, or current. Integral windup occurs when an integral controller continues accumulating error while the actuator is saturated.

A controller may be position-based, velocity-based, or torque-based. In a position-controlled industrial robot, the user may command a trajectory while a manufacturer’s internal servo regulates motor position. In torque control, the external controller directly specifies joint torque, enabling more transparent dynamic and interaction control. Inner loops usually regulate current or velocity at high frequency, while outer loops regulate position, force, or task behaviour at lower frequency.

Joint-Space Position and Motion Control

PID Control

The classical joint-space PID law for independent joints is

τ = Kp e + Ki ∫e dt + Kd ė,

where Kp, Ki, and Kd are proportional, integral, and derivative gain matrices. The proportional term produces a restoring action, the integral term removes persistent bias, and the derivative term provides damping. For a single joint with approximately constant inertia, proportional and derivative feedback can yield a stable second-order response when gains are suitably selected.

In a robot, independent PID control is attractive because it is simple, computationally inexpensive, and often adequate for low-speed motion or robots with embedded compensation. However, it ignores coupling between joints, configuration-dependent inertia, gravity, friction, and velocity-dependent forces. Its performance can deteriorate during fast motion, large payload changes, or highly coupled configurations.

Derivative action should generally be applied to measured velocity or to a filtered error rather than to an unfiltered position error. Numerical differentiation amplifies sensor noise. Integral action requires anti-windup, such as conditional integration, back calculation, or integral clamping. Gain scheduling may be used when the robot dynamics vary substantially with posture or payload.

Gravity and Motion Feedforward

A more effective law augments feedback with model-based terms:

τ = Kp e + Kd ė + g(q) + τff,

where τff may include an estimate of inertia, Coriolis effects, friction, or desired acceleration. Gravity compensation is particularly useful for slow positioning because the feedback controller no longer needs to sustain the robot’s weight through a large position error. Motion feedforward anticipates the torque needed to produce desired acceleration and velocity.

Feedforward cannot correct modelling errors by itself. An incorrect payload estimate, friction model, or acceleration profile produces residual error, which feedback must remove. The best practical architecture is therefore usually model-based feedforward combined with robust feedback.

Computed-Torque and Nonlinear Control

Computed-torque control, also called inverse-dynamics control, uses the robot model to cancel nonlinear dynamics. A common law is

τ = M(q)[q̈d + Kd(q̇d − q̇) + Kp(qd − q)] + C(q,q̇)q̇ + g(q).

If the model is exact and external disturbances are absent, the closed-loop error approximately becomes

ë + Kd ė + Kp e = 0,

which is a linear, decoupled error system. Positive-definite gains can be selected to achieve desired damping and natural frequency.

The main advantage is improved tracking over a wide range of configurations and speeds. The principal limitation is model dependence. Errors in mass, centre of gravity, friction, flexible transmissions, or external loading prevent exact cancellation. The controller should therefore retain feedback margins and avoid excessively aggressive gains. Computed torque also requires reliable estimates of q̇ and q̈d and sufficient computational capacity.

A related approach is partial feedback linearisation, in which only selected dynamic terms are compensated. This may be preferable when the full model is uncertain or computationally expensive. Passivity-based control uses the energy structure of mechanical systems to achieve stable behaviour without relying on perfect cancellation. It is especially relevant where guaranteed safe interaction is more important than maximum trajectory precision.

Task-Space Control

Joint-space control is natural when the task is specified by joint angles. Many applications, however, require the tool centre point to follow a Cartesian path or maintain a particular orientation. Let x = f(q) denote the task-space pose and let J(q) be the geometric Jacobian. The velocity relationship is

ẋ = J(q)q̇.

A task-space error may be defined using translational error and an orientation error, often represented by an axis-angle vector or a quaternion-based error. A desired task-space wrench F is related approximately to joint torque by

τ = Jᵀ(q)F.

A task-space proportional–derivative controller can be written conceptually as

F = Kx ex + Dx ėx + Fff,

followed by τ = JᵀF, with gravity and dynamic compensation added as required. This approach makes the control objective physically meaningful: the designer specifies Cartesian stiffness, damping, or force rather than tuning each joint independently.

Near a kinematic singularity, J loses rank and small Cartesian commands may require very large joint velocities or torques. Damped least-squares inverse kinematics replaces a direct inverse with a regularised solution, reducing sensitivity at the cost of some tracking error. Redundant robots also require null-space control to satisfy secondary objectives such as joint-limit avoidance, collision avoidance, or posture optimisation.

Force and Interaction Control

Position control is insufficient when the robot contacts a surface, inserts a component, polishes a part, or assists a person. Contact tasks require control of mechanical interaction.

Force Control

In explicit force control, a force sensor or an observer measures contact force and the controller attempts to track a desired value. A simple force-feedback law is

v = vf + Kf(Fd − F),

where vf is a nominal velocity command and Kf is a force gain. The effectiveness of this approach depends strongly on environment stiffness, sensor bandwidth, filtering, and contact dynamics. High gains may cause oscillation when the environment is rigid or when sensing and communication introduce delay.

Hybrid position–force control partitions task directions into those regulated by position and those regulated by force. For example, a tool may follow a prescribed path tangentially while maintaining a specified normal force against a surface. The partition must be consistent with the contact geometry; attempting to impose incompatible position and force commands in the same direction leads to conflict.

Impedance and Admittance Control

Impedance control specifies a dynamic relationship between motion deviation and applied force. In a simplified form,

M_d(ẍ − ẍd) + D_d(ẋ − ẋd) + K_d(x − xd) = Fext − Fd.

The robot is made to behave like a virtual mass–damper–spring system. A stiff impedance resists displacement but may be unsafe or unstable during contact. A compliant impedance permits motion in response to external force and is useful for assembly and physical human–robot interaction.

Admittance control measures force and generates a motion command; impedance control generally generates force or torque in response to motion deviation. Admittance is often suitable for robots with accurate position interfaces but limited direct torque control. Impedance is more natural for torque-controlled robots. Neither method eliminates the need to consider environment dynamics, delay, saturation, and energy exchange.

Adaptive and Robust Control

Robot parameters can change because of payload variation, tool exchange, wear, temperature, or uncertain friction. Adaptive control estimates unknown parameters online and updates the control law. In adaptive inverse dynamics, a regressor form such as Y(q,q̇,q̈)θ is used, where θ contains inertial and other physical parameters. An adaptation law modifies the parameter estimate based on tracking error.

Adaptive control can improve performance when uncertainty has a structured parametric form. It may, however, react poorly to unmodelled dynamics, noisy measurements, insufficient excitation, or rapidly changing conditions. Parameter estimates need not converge to their true physical values unless suitable excitation and identifiability conditions are satisfied; bounded tracking may be the more realistic objective.

Robust control seeks acceptable performance despite bounded uncertainty and disturbances. Sliding-mode control, for example, drives the system toward a designed sliding surface and can provide strong disturbance rejection. Its discontinuous switching action may cause chattering, which can excite unmodelled flexible modes and damage actuators. Boundary layers or higher-order sliding methods reduce chattering but introduce approximation effects.

H-infinity and related frequency-domain methods formulate performance in the presence of worst-case disturbances. Model uncertainty can also be represented through structured uncertainty models. Robust methods offer formal guarantees but may require conservative designs and advanced modelling. In industrial practice, robust feedback, saturation management, disturbance observers, and carefully validated feedforward are often combined rather than selecting one method in isolation.

Model-Predictive Control

Model-predictive control (MPC) repeatedly solves a finite-horizon optimisation problem. At each sample, it predicts future motion using a model, minimises a cost function, applies only the first control action, and then updates the prediction using new measurements. A typical cost penalises tracking error, control effort, velocity, and constraint violations.

The major attraction of MPC is its explicit treatment of constraints such as torque, joint position, joint velocity, collision margins, and actuator rate. It can coordinate multiple joints and incorporate changing task objectives. Nonlinear MPC is powerful for complex robot dynamics, but its optimisation burden may challenge real-time implementation. Linear or locally linear MPC, explicit MPC, and fast quadratic-programming solvers reduce this burden.

MPC does not automatically guarantee safety or stability. Terminal costs, terminal constraints, robust formulations, control-barrier constraints, or verified fallback controllers may be required. Model mismatch and delayed state estimates must also be addressed. MPC is therefore most valuable when constraints and multivariable coordination dominate the problem, provided the computational architecture can meet hard deadlines.

Stability, Robustness, and Real-Time Performance

Stability analysis determines whether errors remain bounded and whether they converge. For a linearised closed loop, eigenvalues, gain and phase margins, and frequency-response tools are useful. For nonlinear robot systems, Lyapunov analysis is more appropriate. A candidate energy-like function V(e,ė) should be positive definite, while its derivative should be negative semidefinite or negative definite under the assumed conditions.

The mechanical energy structure of a robot is important: M(q) is positive definite, and the relationship between Ṁ and C has a skew-symmetry property that supports passivity analysis. Computed-torque controllers can be shown to be stable under ideal modelling assumptions, while robust or adaptive designs require explicit consideration of uncertainty bounds and parameter updates.

Digital implementation changes the problem. Sampling, zero-order hold, quantisation, sensor filtering, computation time, network delay, and asynchronous clocks introduce phase lag. A controller that is stable in continuous time may become oscillatory after discretisation. The control period must be short relative to the desired bandwidth and the fastest relevant plant dynamics, while leaving sufficient processor margin for worst-case execution time.

A sound implementation process includes:

• specifying sensor, actuator, and communication rates;
• estimating worst-case computation and delay;
• filtering measurements without excessive phase lag;
• enforcing torque, velocity, position, and temperature limits;
• adding watchdogs and a safe state for missed deadlines;
• testing first in simulation, then in low-energy and constrained experiments;
• logging references, states, commands, saturation events, and faults.

Safety must be designed into the control architecture. A supervisory layer may monitor workspace limits, collision estimates, force thresholds, communication health, and controller validity. Safety-rated monitored stop, reduced-speed modes, and emergency stop functions should not depend solely on an experimental high-level controller.

Selecting a Control Architecture

Controller selection should begin with the task and available interfaces rather than with the most sophisticated algorithm. Joint PID with gravity compensation is often appropriate for repetitive, low-speed positioning when the robot vendor exposes only position commands. Computed torque is attractive when an accurate dynamic model and torque interface are available. Task-space control is preferable when Cartesian accuracy or orientation is central. Force or impedance control is required for contact and collaboration. Adaptive or robust methods become important when payload and dynamics are uncertain. MPC is justified when constraints, coupled motion, and preview information provide benefits greater than its computational cost.

A useful engineering decision sequence is:

1. Define controlled variables and acceptable error, force, and safety limits.

2. Identify sensing, actuation, model, and computation capabilities.

3. Establish a simple stable baseline controller.

4. Add gravity and motion feedforward.

5. Introduce task-space, interaction, adaptive, robust, or predictive features only where the baseline is inadequate.

6. Validate stability, saturation behaviour, timing, and fault response under worst-case conditions.

Illustrative Case Study: Force-Controlled Robotic Surface Finishing

Background

Consider an illustrative robotic cell in which a six-axis industrial manipulator carries a polishing tool. The workpiece has a curved surface with dimensional variation between batches. The tool must follow a programmed tangential path while maintaining a nearly constant normal force.

Situation and Problem

A position-only controller produces variable material removal. On high spots, contact force rises sharply; on low spots, the tool loses contact. Increasing position gain does not solve the problem because the workpiece geometry is uncertain and the tool–surface contact is stiff. Excessive gain also creates oscillation when the tool encounters local curvature changes.

Analysis

The task has two distinct requirements. Tangential motion is primarily a position or velocity problem, while normal motion is a force problem. The directions are coupled through the changing surface normal and robot Jacobian. Tool force sensing introduces noise and delay, and the actuator has a finite torque limit. A controller that commands high corrective velocity in response to force error could become unstable or saturate.

Approach and Solution

The cell uses a task-space frame attached to the local surface. Tangential axes receive trajectory control with velocity feedforward. The normal axis uses admittance control: measured normal force is filtered, compared with the desired force, and converted into a compliant displacement correction. Gravity and nominal dynamic compensation are included in the joint torque command. The admittance gains are selected from a desired virtual mass and damping, and the displacement correction is bounded.

A supervisory layer limits tool speed, normal displacement, joint torque, and force. If force exceeds a threshold or the sensor becomes invalid, the robot retracts at a controlled speed. Before production, the controller is tested with different workpiece stiffnesses, path speeds, payload estimates, and sensor delays. Logs are used to identify saturation and contact-loss events.

Outcome

The resulting system preserves tangential path quality while allowing controlled motion normal to the surface. Variation in workpiece geometry is absorbed by compliant motion rather than by large position errors. Performance still depends on force-sensor calibration, filtering, surface-frame estimation, and conservative limits; the controller is not made universally stable merely by selecting a nominal admittance.

Learning Points

The case demonstrates that controller choice follows task structure. It also shows why hybrid objectives, coordinate-frame definition, saturation handling, and supervisory safety are as important as the nominal control equation. A sophisticated interaction controller cannot compensate for poor sensing or an invalid geometric model.

Challenges, Risks, and Common Design Errors

Several failures recur in robotic control projects. Treating a coupled manipulator as a set of independent joints can produce poor tracking during rapid motion. Excessive proportional or derivative gain may excite gearbox compliance, structural vibration, or sensor noise. Integral action without anti-windup can create severe overshoot after saturation. Differentiating noisy position data without filtering can make derivative control unusable.

Other mistakes include neglecting orientation error representation, ignoring Jacobian singularities, assuming a payload model remains valid after tool changes, and evaluating only nominal simulation results. Contact controllers are particularly sensitive to environment stiffness and delay. Force sensors can exhibit bias, drift, cross-axis coupling, and structural vibration. Learned or data-driven components may improve performance but can fail outside the training distribution.

A controller should never be judged solely by average tracking error. Worst-case error, peak force, recovery after disturbance, energy injection, thermal limits, deadline misses, and behaviour during sensor faults are equally important. Validation should include parameter variation, communication interruptions, unexpected contact, and degraded sensing.

Ethical, Professional, and Governance Considerations

Robot control affects physical safety directly. Engineers are responsible for hazard identification, risk reduction, verification, documentation, and compliance with applicable machinery, industrial-robot, collaborative-robot, and functional-safety requirements. Exact standards depend on jurisdiction and application, but the principles of safeguarding, validation, traceability, and human oversight are broadly applicable.

Control software should be version-controlled and changes should be tested against a defined safety case. Data-driven adaptation should have bounded authority and a reliable fallback. In collaborative applications, low average force is not sufficient: unexpected transients, pinch points, restart behaviour, and loss of communication must be considered. Operators should understand the robot’s modes, limitations, and recovery procedures.

Current Developments and Best Practices

Current research and industrial development increasingly combine model-based control with learning. Neural networks may estimate friction, residual dynamics, or contact properties, while a conventional controller preserves stability and limits. Reinforcement learning is being investigated for complex manipulation, but safe exploration, sim-to-real transfer, distribution shift, and formal guarantees remain significant concerns.

Digital twins and high-fidelity simulation support controller tuning, hardware-in-the-loop testing, and predictive maintenance. Event-based sensing, improved torque sensing, real-time Ethernet, and embedded optimisation expand the feasible control bandwidth. Control-barrier functions and safety filters provide a formal mechanism for modifying commands that would violate constraints.

Best practice is not to replace sound control engineering with novelty. A reliable workflow combines a validated mechanical and sensor model, a simple stable baseline, explicit limits, real-time measurement, incremental complexity, fault handling, and experimental evidence. The final controller should be explainable enough to diagnose and safe enough to fail predictably.

Chapter Summary

Robot control systems transform desired motion and interaction objectives into actuator commands. Joint-space PID control remains useful because it is simple, but gravity compensation, feedforward, and computed torque improve performance by addressing robot dynamics. Task-space control expresses objectives in Cartesian coordinates and requires careful treatment of Jacobians, orientation, redundancy, and singularities.

Force control regulates contact force directly, whereas impedance and admittance control shape the relationship between motion and force. Adaptive control addresses changing parameters; robust control addresses bounded uncertainty and disturbances; MPC handles multivariable constraints through repeated prediction and optimisation. Every method must be assessed for stability, uncertainty, saturation, delay, computation, and safety. The appropriate design is determined by the task, model quality, sensing and actuation interfaces, and real-time resources—not by algorithmic sophistication alone.

Key Terms

Plant: The physical robot, actuators, transmission, and relevant environment being controlled.

Feedback: Control action based on measured output or state.

Feedforward: A command computed from desired motion or estimated disturbances before error occurs.

Tracking error: The difference between a desired variable and its measured or estimated value.

PID control: Proportional, integral, and derivative feedback used to regulate a variable.

Gravity compensation: Model-based torque intended to balance gravitational loading.

Computed-torque control: Nonlinear inverse-dynamics control that compensates robot dynamics.

Task space: Coordinates describing end-effector position, orientation, or other task variables.

Jacobian: Matrix relating joint velocities to task-space velocities.

Singularity: A configuration in which the Jacobian loses rank and motion control becomes ill-conditioned.

Wrench: A combined vector of force and moment.

Hybrid position–force control: Control that assigns position regulation and force regulation to different task directions.

Impedance control: Regulation of a desired dynamic relationship between motion and interaction force.

Admittance control: Conversion of measured force into a compliant motion command.

Adaptive control: Control that updates parameters or laws in response to changing system behaviour.

Robust control: Design intended to maintain performance despite bounded uncertainty or disturbances.

Model-predictive control: Receding-horizon optimisation using a model and explicit constraints.

Actuator saturation: Operation at the physical limit of torque, current, velocity, or displacement.

Integral windup: Excessive accumulation of integral error during actuator saturation.

Control bandwidth: Frequency range over which the closed loop tracks commands effectively.

Review Questions

Short Answer Questions

1. Distinguish between feedback and feedforward control in a robotic manipulator.

2. Why is gravity compensation useful in low-speed robot positioning?

3. State the velocity relationship represented by the robot Jacobian.

4. Differentiate impedance control from admittance control.

5. What is integral windup, and how can it be reduced?

Long Answer Questions

1. Explain the structure, assumptions, benefits, and limitations of computed-torque control.

2. Discuss how task-space control differs from joint-space control, including the roles of the Jacobian and singularities.

3. Compare force control, hybrid position–force control, impedance control, and admittance control for contact tasks.

4. Explain how adaptive and robust control address uncertainty in robot dynamics.

5. Describe the requirements for stable and reliable real-time implementation of a digital robot controller.

Analytical / Application Questions

1. A manipulator tracks slowly under gravity but exhibits large errors during rapid motion. Diagnose the likely causes and propose a staged control improvement.

2. Design a control architecture for a robot inserting a peg into a hole with uncertain position and stiffness. Identify the controlled directions, sensing requirements, and safety limits.

3. A Cartesian controller becomes unstable near a robot singularity. Explain why this occurs and recommend mathematical and supervisory remedies.

22. Multiple Choice Questions with Answers

Question 1

Which term in a PID controller is primarily responsible for removing persistent steady-state error caused by a constant load?

A. Proportional term

B. Integral term

C. Derivative term

D. Feedforward term

Correct Answer: B. Integral term

Question 2

The principal purpose of computed-torque control is to:

A. Remove the need for position sensors

B. Cancel or compensate nonlinear robot dynamics using a model

C. Guarantee zero force during contact

D. Convert a Cartesian trajectory into an image

Correct Answer: B. Cancel or compensate nonlinear robot dynamics using a model

Question 3

Near a kinematic singularity, a Cartesian command may require very large joint velocities because:

A. The gravity vector becomes zero

B. The Jacobian becomes ill-conditioned or loses rank

C. Integral action is automatically disabled

D. The robot has infinite actuator bandwidth

Correct Answer: B. The Jacobian becomes ill-conditioned or loses rank

Question 4

Which control strategy is most directly suited to maintaining a specified normal force while following a tangential surface path?

A. Pure joint position control

B. Hybrid position–force control

C. Open-loop velocity control

D. Unfiltered derivative control

Correct Answer: B. Hybrid position–force control

Question 5

In admittance control, measured external force is generally used to generate:

A. A motion or displacement command

B. A new robot mass matrix only

C. A sensor calibration constant

D. A fixed emergency-stop signal

Correct Answer: A. A motion or displacement command

Question 6

A major risk of excessive derivative gain in a robot controller is that it may:

A. Eliminate all sensor noise

B. Amplify measurement noise and excite vibration

C. Prevent gravity from acting on the robot

D. Make actuator saturation impossible

Correct Answer: B. Amplify measurement noise and excite vibration

Question 7

Which feature is a principal advantage of model-predictive control?

A. It requires no model of the robot

B. It explicitly handles constraints within a prediction and optimisation process

C. It always has lower computational cost than PID

D. It operates without feedback

Correct Answer: B. It explicitly handles constraints within a prediction and optimisation process

Question 8

Why is anti-windup required in a practical PID controller?

A. To prevent the integral state from growing excessively during actuator saturation

B. To increase the robot’s number of degrees of freedom

C. To remove the need for derivative filtering

D. To make the Jacobian square

Correct Answer: A. To prevent the integral state from growing excessively during actuator saturation

Question 9

Which statement best describes robust control?

A. It assumes all physical parameters are known exactly

B. It seeks acceptable performance despite bounded uncertainty and disturbances

C. It uses only integral feedback

D. It is limited to force sensors

Correct Answer: B. It seeks acceptable performance despite bounded uncertainty and disturbances

Question 10

In the surface-finishing case, admittance control was applied mainly because it:

A. Allowed force deviations to produce bounded compliant motion

B. Removed the need for a surface coordinate frame

C. Guaranteed perfect material removal regardless of sensing

D. Replaced all tangential trajectory control

Correct Answer: A. Allowed force deviations to produce bounded compliant motion