Assessment Package: Module 07 - Manipulation

Assessment Overview

Component	Weight	Format	Duration
Theory Quiz	15%	Multiple choice + analysis	45 minutes
Lab Exercises	35%	Python implementations	3 labs
Simulation Project	35%	Complete manipulation system	1 week
Ethics Discussion	15%	Written reflection	500 words
Total	100%

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Theory Quiz

Time Limit: 45 minutes Passing Score: 70% Attempts: 2

Section A: Multiple Choice (40 points)

Q1. Force closure in grasping means:

• a) The gripper is fully closed
• b) Contact forces can resist any external wrench
• c) The grasp uses friction
• d) The object cannot rotate

Q2. A parallel jaw gripper can achieve force closure on a sphere:

• a) Always, regardless of friction
• b) Only with sufficient friction
• c) Never, even with infinite friction
• d) Only if the sphere is deformable

Q3. In impedance control, increasing stiffness K will:

• a) Make the robot more compliant
• b) Increase tracking error
• c) Make the robot resist perturbations more strongly
• d) Reduce contact forces

Q4. The grasp matrix G relates:

• a) Joint torques to end-effector force
• b) Contact forces to object wrench
• c) Object position to finger positions
• d) Friction coefficient to normal force

Q5. For a 3-finger grasp on a planar object to achieve force closure, the minimum number of friction cone edges required is:

• a) 3
• b) 4
• c) 6
• d) Force closure is impossible with 3 frictionless contacts

Q6. In hybrid position/force control, the selection matrix S determines:

• a) Which fingers are active
• b) Which DOFs use force vs. position control
• c) The friction coefficient
• d) The grasp quality metric

Q7. The ε-metric (epsilon metric) for grasp quality measures:

• a) The number of contact points
• b) The largest perturbation wrench the grasp can resist
• c) The friction coefficient
• d) The grasp matrix rank

Q8. In-hand manipulation differs from regrasping because:

• a) The object is never released
• b) Only one finger moves at a time
• c) Force control is not used
• d) The object is always rotated

Q9. A collaborative robot should use impedance control instead of pure position control because:

• a) It's more accurate
• b) It's faster
• c) Contact forces are bounded by stiffness
• d) It uses less energy

Q10. The Jacobian transpose method for force control:

• a) Is exact for any robot configuration
• b) Assumes static equilibrium
• c) Requires force sensor on each joint
• d) Only works for planar robots

Section B: Analysis Problems (60 points)

Q11. (20 points) A planar two-finger grasp contacts a circular object at points p₁ = (-r, 0) and p₂ = (r, 0), where r = 0.05m. The contact normals point toward the object center.

a) Write the grasp matrix G for this configuration (3×4 matrix for 2D). b) What is the rank of G? What wrench space dimension is controllable? c) If friction coefficient μ = 0.3, can this grasp resist a horizontal force of 1N applied to the object center? Show your analysis.

Q12. (20 points) An impedance controller has parameters K = 500 N/m and D = 50 Ns/m. The desired position is x_d = 0.5m.

a) If the current position is x = 0.48m and velocity is ẋ = 0.1 m/s, what force does the controller command? b) The robot contacts a rigid wall at x = 0.49m. What is the steady-state contact force? c) If we want maximum contact force of 20N, what stiffness K should we use?

Q13. (20 points) A manipulation task requires inserting a peg (radius 10mm) into a hole (radius 10.5mm). The peg and hole have alignment error of up to 2mm.

a) Can pure position control complete this task? Why or why not? b) Describe how impedance control enables this task. c) What compliance parameters would you recommend for the Z-axis (insertion direction) vs. XY-axes (alignment correction)?

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Lab Exercises

Lab 07-01: Basic Grasping (30% of lab grade)

Grading Rubric:

Criterion	Excellent (90-100%)	Proficient (70-89%)	Developing (50-69%)	Beginning (Below 50%)
Grasp Pose Generation	Multiple valid grasps, considers object geometry	Single grasp approach works	Grasp often fails	Cannot generate grasps
Gripper Control	Smooth approach, proper grip force	Working but jerky motion	Inconsistent control	Non-functional
Pick Execution	Reliable pick across test objects	Occasional failures	Frequent failures	Cannot complete pick
Quality Evaluation	Contact metrics properly computed	Basic metrics work	Partial implementation	No evaluation
Code Quality	Well-structured, documented	Functional code	Partially working	Non-functional

Lab 07-02: Force Control (35% of lab grade)

Grading Rubric:

Criterion	Excellent (90-100%)	Proficient (70-89%)	Developing (50-69%)	Beginning (Below 50%)
Impedance Control	Correct implementation, tunable parameters	Working with fixed parameters	Partially working	Non-functional
Force Controller	PI force regulation within 10% error	Force regulation within 20%	Oscillatory or >20% error	Cannot regulate
Surface Following	Maintains contact through complex path	Works on simple paths	Frequent contact loss	Cannot follow
Analysis	Quantitative comparison of control modes	Basic comparison	Incomplete analysis	No analysis
Documentation	Clear explanation of tuning process	Basic documentation	Missing sections	No documentation

Lab 07-03: Dexterous Manipulation (35% of lab grade)

Grading Rubric:

Criterion	Excellent (90-100%)	Proficient (70-89%)	Developing (50-69%)	Beginning (Below 50%)
Finger Kinematics	All fingers working, proper Jacobians	Most fingers working	Some fingers working	Non-functional
Grasp Analysis	Force closure verified, ε-metric computed	Contact extraction works	Partial analysis	Cannot analyze
Multi-Finger Control	Coordinated grasp on multiple objects	Works on single object	Inconsistent	Non-functional
In-Hand Manipulation	Object rotation >45° while grasped	Some rotation achieved	Object often dropped	Cannot manipulate
Integration	Complete pick-manipulate sequence	Partial sequence	Individual pieces work	Non-functional

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Simulation Project

Project: Autonomous Pick-and-Place System

Objective: Build a complete manipulation pipeline that can pick objects from a table, manipulate them if needed, and place them at specified locations.

Duration: 1 week Deliverables: Code repository + 4-page technical report

Requirements

1. Perception Integration (20%)

   • Use simulated camera to detect objects
   • Estimate object pose for grasp planning
   • Handle multiple objects in scene

2. Grasp Planning (25%)

   • Generate multiple grasp candidates per object
   • Rank grasps by quality metric
   • Select grasp considering robot reachability

3. Motion and Manipulation (30%)

   • Plan collision-free approach motion
   • Execute grasp with force feedback
   • Regrasp or adjust if initial grasp fails

4. Task Execution (25%)

   • Complete pick-and-place for 5 different objects
   • Handle task failures gracefully
   • Report success/failure and timing metrics

Object Set

The system must handle:

1. Box (6cm × 4cm × 3cm) - Easy
2. Cylinder (radius 2.5cm, height 8cm) - Easy
3. Sphere (radius 3cm) - Medium
4. Irregular shape (provided mesh) - Medium
5. Thin plate (10cm × 8cm × 0.5cm) - Hard

Grading Rubric

Criterion	Points	Description
Perception	20	Object detection and pose estimation
Grasp Planning	25	Quality-ranked candidate generation
Execution	30	Reliable grasp, manipulation, place
Robustness	15	Failure handling, multiple attempts
Report	10	Clear writing, quantitative results
Total	100

Evaluation Scenarios

Each object is tested in 3 positions:

• Center of workspace (easy reach)
• Edge of workspace (challenging IK)
• Near other objects (collision avoidance)

Success criteria: Object placed within 2cm of target position, upright orientation.

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Ethics Discussion

Prompt

In a 500-word reflection, address the following scenario:

A robotics company is developing a home assistant robot capable of manipulation tasks—opening doors, loading dishwashers, handling groceries, etc. During testing, the following incident occurs:

The robot is asked to "clear the table." On the table are:

• Dirty dishes (should be put in dishwasher)
• A newspaper (should be recycled or kept)
• Grandmother's antique teacup (extremely fragile, irreplaceable)
• A laptop computer (expensive, contains data)
• A half-eaten sandwich (trash or keep?)

The robot proceeds to grasp the antique teacup with force calibrated for normal ceramics, and it breaks. The family is devastated.

Address the following:

1. What safeguards might have prevented this incident? Consider both technical (sensing, force control) and process (user confirmation) approaches.

2. Who bears responsibility for the broken teacup? The robot company? The user who gave the command? The person who left the teacup on the table?

3. Should manipulation robots have "categories of caution"—object types that require human confirmation before handling? How would you define these categories?

4. How should the robot communicate uncertainty about object handling? The teacup might have looked similar to a regular cup. What signals should prompt extra caution?

Rubric

Criterion	Excellent (90-100%)	Proficient (70-89%)	Developing (50-69%)	Beginning (Below 50%)
Technical Safeguards	Multiple specific solutions with tradeoffs	Several reasonable safeguards	One or two ideas	No concrete proposals
Responsibility Analysis	Nuanced consideration of all parties	Considers multiple parties	Single party blamed	Avoids the question
Category Design	Specific, practical categories with examples	General categories	Vague categorization	No categories
Uncertainty Communication	Multiple modalities, user-centered design	Basic communication approach	Generic suggestions	Ignores communication
Writing Quality	Clear, organized, persuasive	Clear with minor issues	Some clarity problems	Unclear or incomplete

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Answer Key (Instructor Access Only)

Quiz Answers

Section A:

1. b) Contact forces can resist any external wrench
2. b) Only with sufficient friction
3. c) Make the robot resist perturbations more strongly
4. b) Contact forces to object wrench
5. d) Force closure is impossible with 3 frictionless contacts
6. b) Which DOFs use force vs. position control
7. b) The largest perturbation wrench the grasp can resist
8. a) The object is never released
9. c) Contact forces are bounded by stiffness
10. b) Assumes static equilibrium

Section B:

Q11: a) Grasp matrix for 2D (forces create wrench on object):

Contact 1 at (-r, 0), normal = (1, 0):

• Force contribution: (1, 0)
• Torque contribution: (-r × 0) - (0 × 1) = 0

Contact 2 at (r, 0), normal = (-1, 0):

• Force contribution: (-1, 0)
• Torque contribution: (r × 0) - (0 × -1) = 0

G = | 1 0 -1 0 | | 0 1 0 1 | | 0 0 0 0 |

(Note: This shows the grasp cannot control torque—needs friction)

b) Rank(G) = 2. Only translational forces controllable, not torque.

c) With μ = 0.3, each contact can apply tangential force up to 0.3×N.

• For 1N horizontal force, need contact to provide 0.5N tangential force
• This requires normal force N ≥ 0.5/0.3 = 1.67N per contact
• Yes, achievable with sufficient grip force

Q12: a) F = K(x_d - x) - D(ẋ) = 500(0.5 - 0.48) - 50(0.1) = 10 - 5 = 5N

b) At steady state, x = 0.49m, ẋ = 0: F = 500(0.5 - 0.49) - 0 = 5N (pushing against wall)

c) For max 20N: K(x_d - x_wall) ≤ 20 K(0.5 - 0.49) ≤ 20 K ≤ 20/0.01 = 2000 N/m

Q13: a) No. Position control would jam against hole edges due to 2mm misalignment (larger than 0.5mm clearance). The robot would apply excessive force trying to reach the commanded position.

b) Impedance control allows the peg to "feel" the hole edges and comply. Low XY stiffness lets misalignment self-correct as the peg slides along chamfers/edges.

c) Recommended parameters:

• Z-axis (insertion): Higher stiffness (500-1000 N/m) for positive insertion motion
• XY-axes (alignment): Low stiffness (50-100 N/m) to allow compliance with hole edges
• Rotation: Low stiffness to allow angular correction

This is sometimes called "Remote Center Compliance" (RCC) when mechanically implemented.

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