ME 449 Robotic Manipulation (Archive 2012)

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Spring Quarter 2012


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 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 (free pdf download); Chapter 27 "Contact Modeling and Manipulation," I. Kao, K. Lynch, and J. Burdick, from the Springer Handbook of Robotics; and other sources.


Final Project

Find information on the final project here.

Approximate Syllabus


Representations of motion
Reading: Mason pp. 1-19, 41-47, 58-60, Chapter 4; Choset chapter 3.5; Murray Li Sastry pp. 19-61 (through Section 4; you can skip Section 2.3 on "Other representations")
* 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 points, and change frames
* velocity and acceleration as time-derivatives of SE(3); skew-symmetric matrix representation
* adjoint transformation, changing coordinate frames
* body frame and world frame velocity; hybrid velocity
* rigid body motion expressed as translation along, and rotation about, an axis; twists and screws; exponential map
* planar simplification: SE(2) and se(2) and 3 coordinates; rotation centers (finite motions) and instantaneous centers (velocities)
* C-space obstacles (2R robot and planar body); motion planning: potential fields, search trees, kinematic motion planning (depth-first, breadth-first, and best-first planning; NHP; RRT), software packages (OOPSMP and MSL); optimization approaches
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 (purely kinematic or using wrenches)


Representations of forces (readings: MLS pp. 61-9, Mason ch 5)
* forces and moment; wrenches; lines of action
* adjoint transformation and changing frames (derived from coordinate-free power)
* combinations of forces and polyhedral convex wrench cones
* force closure
* planar case: moment labeling and planar force closure; equivalence of first-order form closure and frictionless force closure
Contact modeling with friction (Mason ch 6)
* 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
* stability of a frictionless assembly; adding friction
* 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: stability of assembly, pipe clamp, meter stick, toppling (pushing a can), peg-in-hole, etc.
Planar contact patches, limit surfaces, and pushing (Mason ch 6.6, 7.2, 7.3)
* limit surface
* pushing


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


* 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


* Routh-Wang-Mason, Newton, Poisson, and Stronge restitution coefficients
* 3D impact
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