Unit 2: Specifications of Robot

I. Orientation — Robot Performance and Its Measurement

Robot specifications describe how closely and consistently a robot can produce commanded motion under stated operating conditions. In laboratory testing, Sierena's utility robot U-BOT is commanded to reach known positions or execute defined movements; measured results are then compared with commands to estimate performance.

• Central principle: A specification is meaningful only when the test conditions, measurement method, units, number of trials, robot configuration, speed, and payload are stated.
• Reference quantity: Measurements are normally associated with the tool centre point (TCP), end-effector tip, or a clearly marked point on the U-BOT.
• Coordinate convention: Position is expressed in a selected frame as (x), (y), and (z), usually in millimetres; orientation may be expressed in degrees or radians.
• Required distinction:
  • Accuracy concerns closeness to the commanded or true value.
  • Repeatability concerns closeness among repeated outcomes.
  • Resolution concerns the smallest detectable or commandable change.
• Statistical convention: Repeated measurements are represented by their mean, range, and standard deviation rather than by a single observation.
• Controlled conditions: Supply voltage, mounting, warm-up state, payload, approach direction, joint configuration, speed, and environmental conditions should remain constant.
• Measurement tools: Depending on required precision, use a steel rule, vernier calliper, dial indicator, digital displacement sensor, protractor, camera-calibration system, or coordinate-measuring device.
• Safety condition: Tests must remain within the U-BOT’s documented joint, payload, velocity, and workspace limits; an emergency-stop facility should remain accessible.

II. U-BOT Experimental Method — Establishing a Reliable Test

A. Estimation of accuracy, repeatability, resolution, and other specifications of robot using Sierena's utility robot U-BOT

The experiment estimates U-BOT performance by comparing programmed motion with independently measured end-effector motion.

• Preparation: Mount U-BOT on a rigid, level surface and inspect its joints, links, end-effector, cables, and emergency-stop control.
• Reference frame: Define a robot-base frame and identify the TCP; place a calibrated scale, graph sheet, target plate, or dial indicator relative to that frame.
• Warm-up: Execute several low-speed cycles before recording data so that lubrication, motor temperature, and controller behaviour become reasonably stable.
• Test command: Program U-BOT to move from a fixed home pose to selected target poses distributed across the useful workspace.
• Repeated sampling: For each target, conduct at least several trials—commonly ten or more—and always approach from the same direction unless backlash is being investigated.
• Data record: Tabulate commanded coordinates, measured coordinates, trial number, payload, speed, approach direction, and observed error.
• Independent measurement: Do not infer performance solely from the robot controller’s displayed coordinates; these generally represent commanded or encoder-estimated values, not an external measurement.
• Result format: Report linear quantities in millimetres, angular quantities in degrees, speed in millimetres per second or degrees per second, and payload in kilograms.

B. Measurement Quality and Experimental Controls

A valid specification requires measurement uncertainty to be smaller than the robot performance being estimated.

• Instrument resolution: If a scale reads only to (1\ \text{mm}), it cannot reliably distinguish robot errors of (0.1\ \text{mm}).
• Zero setting: Establish and verify instrument zero before and after the experiment; a shifted zero introduces systematic error.
• Parallax control: Read scales perpendicular to the graduation or use a digital sensor to avoid observer-dependent displacement.
• Configuration control: Use the same joint configuration for repeated Cartesian targets because different configurations can produce different compliance and backlash.
• Uncertainty statement: Record the instrument’s least count and calibration status alongside the result.
• Outlier handling: Retain unusual observations unless a documented cause—such as collision, sensor slip, or communication loss—justifies rejection.

III. Accuracy — Closeness to the Commanded Pose

A. Estimation of accuracy

Accuracy is estimated from the difference between a commanded target and the mean position actually attained by U-BOT.

• Single-axis error: For a commanded coordinate (x_c) and measured coordinate (x_i) in trial (i), the signed error is:

e_i = x_i - x_c

• (e_i): signed position error in millimetres.
• (x_i): measured coordinate in trial (i).
• (x_c): commanded coordinate.

• Mean attained position: For (n) trials:

x̄ = (1/n) Σx_i
E_x = x̄ - x_c

• (\bar{x}): mean measured coordinate.
• (n): number of trials.
• (E_x): systematic accuracy error along the (x)-axis.

• Three-dimensional position error: If the mean attained position is ((\bar{x},\bar{y},\bar{z})) and the target is ((x_c,y_c,z_c)):

E_p = √[(x̄ - x_c)² + (ȳ - y_c)² + (z̄ - z_c)²]

• (E_p): magnitude of position accuracy error.
• (\bar{y},\bar{z}): mean measured (y)- and (z)-coordinates.

• Worked example: If U-BOT is commanded to (x_c=200.0\ \text{mm}) and repeated measurements have mean (\bar{x}=198.8\ \text{mm}), then (E_x=-1.2\ \text{mm}). The attained point falls (1.2\ \text{mm}) short along (x).
• Multiple targets: Test central, boundary, high, low, near-base, and extended-arm positions because accuracy commonly varies throughout the workspace.
• Angular accuracy: Command a known tool angle and calculate measured angle minus commanded angle in degrees.

B. Interpretation and Limitations

Accuracy identifies target-related bias but does not by itself show whether U-BOT moves consistently.

• Systematic causes: Link-length errors, joint-zero offsets, imperfect TCP calibration, frame misalignment, gear backlash, and structural deflection can shift the mean attained pose.
• Load dependence: A heavier end-effector can increase error through link bending, bearing compliance, or actuator loading.
• Direction dependence: Approaching one target from opposite directions may expose backlash or joint friction.
• Calibration use: Consistent signed error can sometimes be reduced by joint-offset, TCP, or coordinate-frame calibration.
• Reporting requirement: State whether accuracy is the signed axis error, absolute axis error, Euclidean position error, or angular error; these values are not interchangeable.

IV. Repeatability — Consistency of Repeated Motion

A. Estimation of repeatability

Repeatability measures the spread of attained positions when U-BOT reaches the same target repeatedly under unchanged conditions.

• Test sequence: Move from the same home pose to the selected target, record the attained position, return home, and repeat the cycle.
• Mean position: Calculate (\bar{x}), (\bar{y}), and (\bar{z}) from all recorded trials.
• Standard deviation: The sample spread along one axis is:

s_x = √[Σ(x_i - x̄)² / (n - 1)]

• (s_x): sample standard deviation along (x), in millimetres.
• (x_i): measured position in trial (i).
• (\bar{x}): mean measured position.
• (n): number of trials.

• Range method: A simple laboratory estimate is (Rx=x{\max}-x{\min}), where (x{\max}) and (x_{\min}) are the largest and smallest readings.
• Three-dimensional spread: Calculate each trial’s radial distance from the mean point:

r_i = √[(x_i - x̄)² + (y_i - ȳ)² + (z_i - z̄)²]

• (r_i): radial deviation of trial (i).
  • Reporting convention: State the chosen measure explicitly—for example, maximum radial deviation, axis range, or (\pm3s). Different conventions produce different numerical specifications.

B. Accuracy versus Repeatability

Accuracy and repeatability are independent aspects of performance and must be contrasted explicitly.

1. High repeatability, low accuracy: Measurements cluster tightly but away from the commanded target; calibration may correct the stable bias.
2. High accuracy, low repeatability: The mean lies near the target, but individual positions are widely scattered; random effects make the robot unreliable for precise placement.

• Likely variation sources: Gear clearance, encoder noise, motor control fluctuations, vibration, thermal change, loose fixtures, and inconsistent approach paths increase spread.
• Practical significance: Assembly, drilling, dispensing, and pick-and-place operations often depend strongly on repeatability because the same taught position must be reproduced over many cycles.
• Test limitation: Repeatability obtained at one pose, speed, and payload must not be assumed to apply throughout the entire workspace.

V. Resolution — Smallest Distinguishable Motion

A. Estimation of resolution

Resolution is the smallest incremental change that U-BOT can command or that the measuring arrangement can reliably detect.

• Command-resolution test: Apply progressively smaller joint or Cartesian increments and observe whether the TCP produces a distinct, repeatable displacement.
• Procedure: Begin with a clearly visible step, reduce the command increment, and identify the smallest step that consistently produces measurable motion above sensor noise.
• Joint resolution: If an encoder produces (N) counts per revolution, the ideal encoder increment is:

θ_res = 360° / N

• (\theta_{res}): angular encoder resolution.
• (N): effective encoder counts per joint revolution.

• Linear effect: For a link moving through a small angular increment (\Delta\theta) radians at effective radius (L):

Δs ≈ LΔθ

• (\Delta s): approximate TCP displacement.
• (L): effective distance from the joint axis.
• (\Delta\theta): angular increment in radians.

• Measurement criterion: The observed displacement should exceed instrument least count and background variation; otherwise only an upper bound on resolution can be reported.
• Workspace dependence: A fixed joint increment produces different Cartesian displacement depending on arm configuration and distance from the joint axis.

B. Commanded, Encoder, and Measurement Resolution

Resolution has several forms that should not be confused.

1. Commanded resolution: The smallest numerical increment accepted by the U-BOT controller or programming interface.
2. Encoder resolution: The smallest joint displacement represented by one effective feedback count.
3. Mechanical resolution: The smallest physical output motion after transmission effects, friction, backlash, and compliance.
4. Measurement resolution: The smallest change distinguishable by the external instrument.

• Limiting rule: The experiment is constrained by the coarsest element in the command–actuation–measurement chain.
• Resolution versus accuracy: A controller may accept (0.1\ \text{mm}) increments while the robot still has several millimetres of absolute position error.
• Resolution versus repeatability: Small command increments do not guarantee that repeated endpoints will form a narrow cluster.

VI. Other Robot Specifications — Functional Performance of U-BOT

A. Estimation of other specifications of robot

Other specifications describe the operating envelope, motion capability, loading capacity, and dynamic behaviour of U-BOT.

• Workspace: Move each joint through safe documented limits and map the reachable TCP positions; report the boundary in millimetres and identify unreachable internal regions.
• Range of motion: Record minimum and maximum angular displacement of each revolute joint in degrees, or linear travel of each prismatic joint in millimetres.
• Maximum speed: Command motion over a measured path and calculate:

v_avg = d / t

• (v_{avg}): average TCP speed.
• (d): measured path length.
• (t): elapsed travel time, excluding or explicitly including acceleration as stated.

• Payload capacity: Increase payload only within approved limits and observe whether U-BOT satisfies chosen position-error, repeatability, temperature, and stability criteria.
• Cycle time: Measure total time for a defined sequence such as home–pick–place–home; include dwell and gripper-operation times when relevant.
• Backlash: Reach the same point from positive and negative directions; the difference between attained positions estimates directional lost motion.
• Drift: Repeat a reference-position measurement after sustained operation; change with time can indicate heating, sensor drift, or structural expansion.
• Degrees of freedom: Count independent controlled joint variables; each revolute or prismatic joint normally contributes one degree of freedom.
• Load effect: Repeat accuracy, repeatability, and speed tests at no load and at a stated payload to reveal compliance and control limitations.

B. Documentation and Validity of Results

A laboratory specification is complete only when another investigator could reproduce its conditions and calculations.

• Test report: Include U-BOT identification, end-effector, software or controller settings, measurement instrument, target coordinates, payload, speed, sample count, and raw readings.
• Graphs: Use scatter plots for repeated positions, error-versus-target plots for accuracy, and payload-versus-error plots for compliance.
• Uncertainty: Avoid reporting more decimal places than supported by the measuring instrument and experimental spread.
• Scope limitation: Laboratory estimates apply to the tested robot, configuration, environment, and procedure; they do not automatically replace manufacturer-rated specifications.
• Safe conclusion: Compare measured values with stated operational requirements only after confirming identical units, coordinate definitions, load conditions, and statistical conventions.