Unit 2: Specifications of Robot - Subjective Questions

Accuracy is the ability of the U-BOT to move its end-effector to the commanded or desired position. Repeatability is the ability of the robot to return to the same position repeatedly under identical operating conditions.

• A robot may have high repeatability but poor accuracy if it reaches the same incorrect position every time.
• A robot may have good accuracy but poor repeatability if its average position is close to the target but individual trials vary considerably.
• Accuracy is affected by calibration, link dimensions, joint offsets, backlash, and controller errors.
• Repeatability is affected by mechanical wear, friction, vibration, temperature, and sensor noise.

Thus, accuracy indicates closeness to the desired point, whereas repeatability indicates consistency of repeated motion.

A suitable procedure for estimating positional accuracy is:

• Select a target point within the robot's specified workspace.
• Record the target coordinates or measure the target location using a suitable reference device.
• Command the U-BOT to move to the target point.
• Measure the actual end-effector coordinates after the robot settles.
• Calculate the error in each coordinate using , , and .
• Compute the resultant positional error as
  
• Repeat the measurement at different points in the workspace.
• Report the maximum, minimum, mean, or root-mean-square error.

The estimated accuracy is commonly stated as the maximum or average distance between the commanded and measured positions. Measurement conditions, payload, tool orientation, and calibration status should also be recorded.

Repeatability can be determined by commanding the U-BOT to reach the same programmed point several times.

• Select a fixed target point and use the same payload, speed, approach direction, and tool configuration for every trial.
• Command the robot to move away from the point and return to it repeatedly.
• Measure the actual position after each return.
• If the measured positions are for trials, calculate the mean position:
  
• Determine the deviation of every measured point from the mean position.
• The spread of the points, maximum deviation, standard deviation, or diameter of the enclosing region may be used to express repeatability.

A smaller spread indicates better repeatability. The result should identify the number of trials and the operating conditions.

Suppose the robot is tested at target points. Let the positional error at point be .

The mean absolute positional error is

If the error has three components, then

The root-mean-square error is obtained by squaring the errors, finding their mean, and taking the square root:

For three-dimensional errors, this becomes

• Mean error indicates the average magnitude of positioning error.
• RMS error gives greater weight to larger errors.
• The maximum error is useful for checking whether the robot satisfies a specified tolerance.

These measures provide a quantitative estimate of U-BOT accuracy over its workspace.

Resolution is the smallest change in a robot input or output that can be detected, commanded, or produced.

• Encoder resolution: The smallest angular movement detected by a joint encoder. If an encoder provides counts per revolution, its ideal angular resolution is
  
• Control resolution: The smallest change in joint command that the controller can generate.
• Spatial resolution: The smallest linear movement of the end-effector that can be commanded or detected at a particular location.

The spatial resolution depends on the joint resolution and robot geometry. It is also influenced by transmission backlash, gear flexibility, calibration, and numerical rounding. High encoder resolution does not automatically guarantee high practical spatial resolution because mechanical errors may be larger than the sensor increment.

For a planar two-link robot with link lengths and , the end-effector coordinates are

For small joint changes, the end-effector displacement is approximated using the Jacobian matrix:

where

If the joint resolutions are and , the approximate spatial resolution can be estimated from the resulting and . The result changes with robot configuration because the Jacobian changes throughout the workspace.

Workspace is the total region that the robot end-effector can reach with at least one allowable configuration. Reachability refers to whether a particular position, and sometimes a particular orientation, can be achieved by the robot.

An experimental investigation can be performed as follows:

• Define safe limits for every U-BOT joint.
• Move the robot through a planned set of joint configurations.
• Record the corresponding end-effector coordinates.
• Plot or tabulate the reachable points.
• Identify boundaries, inaccessible regions, singular regions, and locations where orientation is restricted.
• Repeat the test at different tool orientations if orientation is part of the specification.

The experimentally observed workspace may be smaller than the theoretical workspace because of joint limits, collision restrictions, payload limitations, safety constraints, and controller limitations.

Payload capacity is the maximum load that the robot can safely carry at its specified operating conditions while maintaining acceptable performance.

Payload can affect the U-BOT in the following ways:

• A larger payload increases joint torque and structural deflection.
• Motor acceleration and deceleration may be reduced.
• Gear backlash and elastic deformation can become more significant.
• Positioning accuracy may decrease because the end-effector sags under load.
• Repeatability may decrease if friction, vibration, or settling time increases.
• Excessive payload may cause overheating, overload alarms, or mechanical damage.

Payload tests should use several known masses and should measure the same target point under identical conditions. The results should be compared with the unloaded case and should remain within the manufacturer's rated limits.

• Maximum speed is the highest permitted rate of motion of a robot joint or end-effector, often expressed in degrees per second or millimetres per second.
• Acceleration is the rate at which the robot's velocity changes. High acceleration reduces travel time but may increase vibration and positioning error.
• Cycle time is the time required to complete a specified sequence of motions, including acceleration, deceleration, settling, tool operation, and any programmed delays.

These specifications are related but not identical. A robot with high maximum speed may still have a long cycle time if it accelerates slowly, requires long settling time, or follows a complex path. U-BOT measurements must specify the exact motion sequence, payload, travel distance, and accuracy requirement.

• Backlash is lost motion caused by clearance between mating mechanical parts. It can produce different positions when a target is approached from opposite directions.
• Compliance is elastic deformation in links, joints, gears, or the tool. It increases under payload and causes static deflection.
• Friction opposes motion and may cause stick-slip behavior, especially during small movements.
• Hysteresis means that the output depends on the previous motion history. The same command may produce different positions during forward and reverse approaches.

These effects can reduce accuracy, repeatability, and practical resolution. To study them, the U-BOT should be commanded to approach the same target from different directions and with different payloads. The difference between the measured positions indicates direction-dependent mechanical error.

Calibration establishes the relationship between the robot's commanded joint values and its actual physical position.

A calibration process may include:

• Setting the mechanical zero or home position of each joint.
• Measuring link dimensions and tool offsets.
• Correcting joint-angle offsets and coordinate-frame transformations.
• Verifying the robot at known reference points.
• Updating controller parameters where permitted.

Without calibration, systematic errors may be incorrectly interpreted as random repeatability errors. Calibration generally improves absolute accuracy, but it cannot completely eliminate backlash, friction, vibration, thermal expansion, or load-dependent deformation. Calibration conditions should therefore be documented before estimating U-BOT accuracy.

The experiment should compare repeated-positioning performance at representative central and boundary points.

• Select at least three points near the centre and three points near the workspace boundary.
• Use the same tool, payload, speed, approach direction, and settling time at every point.
• Move the U-BOT away from each point and return to it for a fixed number of trials.
• Measure the end-effector position after every trial.
• Calculate the mean position, maximum deviation, standard deviation, and spread for each point.
• Compare the statistical results for central and boundary points.

A point has better repeatability when its measured positions have a smaller spread. The conclusion should not be based on one point only because robot geometry, singularities, joint loading, and direction of approach can vary across the workspace.

A singularity is a robot configuration in which the Jacobian matrix loses rank. At such a configuration, one or more Cartesian directions cannot be produced normally, or very large joint movements are required for a small end-effector movement.

Near a singularity:

• Small joint errors can produce relatively large Cartesian errors.
• Cartesian resolution becomes direction-dependent.
• Joint velocities may become very high for a commanded Cartesian velocity.
• The robot may move slowly, stop, or generate a controller warning.
• Accuracy and repeatability can deteriorate because the mechanism becomes poorly conditioned.

During laboratory estimation, singular and near-singular configurations should be identified and reported separately. They should not be treated as representative of normal operation unless the experiment specifically investigates them.

The measured position of the U-BOT depends on the coordinate frame and the defined tool centre point.

• The base coordinate system provides the reference origin and axes for reporting position.
• A joint or link coordinate system is attached to a particular robot member.
• The tool coordinate system is attached to the end-effector.
• The tool centre point, or TCP, is the point whose position is controlled and measured.

An incorrect base-frame transformation can shift or rotate all measured coordinates. An incorrect TCP offset can produce a position error even when the robot flange is correctly positioned. Therefore, the experiment must document the coordinate frame, TCP dimensions, units, axis directions, and orientation convention before estimating accuracy or resolution.

A robot link transformation can be represented by a homogeneous matrix

where is a rotation matrix and is a position vector.

For a robot with links, the end-effector pose relative to the base is

The final matrix has the form

• gives the end-effector orientation.
• gives the end-effector position.
• The matrices may be constructed using the Denavit-Hartenberg parameters of the U-BOT.

Comparing calculated from the robot model with the experimentally measured TCP position gives the model-based positioning error.

Static accuracy is the positioning performance measured after the robot has reached a commanded point and has settled. It mainly reflects calibration, geometry, joint offsets, backlash, and static deformation.

Dynamic accuracy is the tracking performance while the robot is moving along a path or performing a motion at a specified speed and acceleration. It is affected by:

• Controller sampling and interpolation delay.
• Motor and drive response.
• Vibration and structural flexibility.
• Payload and acceleration.
• Path curvature and changes in direction.

A U-BOT may show acceptable static accuracy but poor dynamic accuracy because it cannot follow a fast trajectory exactly. Both forms should be tested separately when evaluating the robot for laboratory or manufacturing applications.

For position repeatability:

• Command the U-BOT to return to the same TCP position for several trials.
• Record , , and for each trial.
• Calculate the mean position and the deviation or standard deviation of each coordinate.

For orientation repeatability:

• Maintain the same target orientation for every trial.
• Record orientation using the robot's specified representation, such as roll-pitch-yaw angles or a rotation matrix.
• Calculate the angular difference between each measured orientation and the mean orientation.

The overall result may be reported as a maximum translational deviation and maximum angular deviation. Position and orientation should be analysed separately because a robot can repeat position accurately while showing greater variation in wrist orientation. Approach direction and tool mounting must remain constant.

Measurement uncertainty is the range within which the true value is expected to lie. If the measurement instrument has an uncertainty comparable to the robot error, the calculated specification may not be reliable.

Uncertainty can be reduced or controlled by:

• Using a calibrated measuring instrument with suitable resolution.
• Rigidly mounting the reference device and target fixture.
• Repeating measurements and using statistical estimates.
• Controlling temperature, vibration, lighting, and external disturbances.
• Allowing the robot and instruments to reach thermal equilibrium.
• Keeping payload, tool mounting, speed, and approach direction constant.
• Reporting instrument uncertainty along with the measured robot error.

The observed error is a combination of robot error and measurement error. Therefore, the laboratory report should distinguish measured performance from the uncertainty of the measurement process.

Theoretical specifications are obtained from the robot's geometry, joint limits, encoder data, controller parameters, and manufacturer information. Experimental specifications are obtained by measuring actual robot behaviour.

• Theoretical workspace may be larger than the usable workspace because it may not include collision and safety restrictions.
• Theoretical resolution may be finer than practical resolution because backlash and friction are excluded.
• Theoretical accuracy may assume perfect calibration and rigid links.
• Experimental repeatability includes mechanical wear, sensor noise, vibration, and environmental effects.
• Manufacturer values may apply only to specified payload, speed, temperature, and test procedures.

A meaningful comparison requires identical definitions, units, operating conditions, and measurement methods. Differences between theory and experiment should be explained rather than simply treated as experimental failure.

Robot performance can change as the mechanism operates and its components warm up.

• Motors, gearboxes, and bearings generate heat during operation.
• Thermal expansion changes link dimensions and joint relationships.
• Lubricant viscosity and friction may change with temperature.
• Sensor offsets and electronic characteristics may drift.
• Long operation can increase repeatability variation if components become hot.

A valid test should specify the initial temperature, warm-up procedure, operating duration, and ambient conditions. Measurements can be taken before warm-up, after a defined warm-up period, and during extended operation. If the measured error changes significantly, temperature is an important factor in the robot's practical accuracy specification.