ME 449 Robotic Manipulation (Archive 2012)

Spring Quarter 2012

• Instructor: Prof. Kevin Lynch
• Meeting: 12:30-1:50, Tues Thurs, LG72

Course Summary

Mechanics of robotic manipulation, computer representations and algorithms for manipulation planning, and applications to industrial automation, parts feeding, grasping, fixturing, and assembly.

Grading

Grading for the course will be based on problem sets and a final project. There will be no exams. The final project, due during finals week, will take the form of a conference paper analyzing a manipulation problem, building on another research paper, or implementing a simulation.

Course Text

Mechanics of Robotic Manipulation, M. T. Mason, MIT Press, Cambridge, MA, 2001, ISBN 0-262-13396-2.

Supplementary material will come from Principles of Robot Motion, H. Choset et al., MIT Press 2005; A Mathematical Introduction to Robotic Manipulation, R. M. Murray, Z. Li, and S. S. Sastry, CRC Press, 1994, ISBN 0-8493-7981-4; Chapter 27 "Contact Modeling and Manipulation," I. Kao, K. Lynch, and J. Burdick, from the Springer Handbook of Robotics; and other sources.

Approximate Syllabus

KINEMATICS

Representations of motion

• degrees of freedom
• configuration space
• coordinates and constraints, holonomic and nonholonomic
• orientation from coordinates of three points minus six constraints; rotation matrix SO(3)
• rigid-body positions: SE(3) (other representations include Euler angles, quaternions)
• using SE(3) to represent configurations, displace configurations, and change frames
• velocity and acceleration as time-derivatives of SE(3)
• adjoint transformation, changing coordinate frames
• velocity in body-frame and world-frame
• planar simplification: SE(2) or 3 coordinates, rotation centers

Representations of surfaces

• piecewise-smooth parametric curves and surfaces: 2D and 3D
• differential forms and their relationship to parametric representations: 2D and 3D

Contact constraints

• nth-order conditions for free motion, penetration, roll-slide, and rolling
• multiple contacts: partitioning velocities and accelerations according to the constraints; contact modes
• polyhedral convex sets (polytopes) and polyhedral convex cones
• planar case (Reuleaux's method)
• grasping and fixturing: first- and second-order form closure and the number of contacts needed
• rolling motion planning
• other contact constraint types: point contact with friction, soft-finger. can deal with both purely kinematically, or introduce wrenches, as discussed below.

FORCES

Representations of forces

• forces and moment; wrenches
• adjoint transformation and changing frames
• combinations of forces and polyhedral convex wrench cones
• planar case: moment labeling

Contact modeling with friction

• zero friction, normal force only; multiple contacts; duality of force and motion freedoms
• Coulomb friction and duality of force and motion freedoms
• grasping and fixturing: force closure; equivalence of first-order form closure and frictionless form closure; number of contacts needed
• pyramid approximations and linear programming test for force closure; planar friction cones and moment labeling test for force closure

Static and quasistatic manipulation

• static equilibrium (zero acceleration forces)
• wedging and jamming
• quasistatic rigid-body mechanics solutions: consistent {motion, wrench} pairs
• ambiguity and inconsistency
• planar problems: Reuleaux and moment labeling
• examples: pipe clamp, meter stick, toppling, peg-in-hole, etc.

Planar contact patches, limit surfaces, and pushing

• limit surface
• pushing

MANIPULATOR CONTROL MODELS

Motion, force, hybrid, and impedance control models, DOF for each contact, internal forces, kinematic deficiency

DYNAMICS

• rigid-body dynamics, inertia matrix, Newton-Euler equations
• solving rigid-body dynamics problems with friction and different manipulator control models
• inconsistent specification of controls
• complementarity formulations and simulation
• examples

IMPACT

• Newton, Poisson, and Stronge restitution coefficients
• 3D impact