Syllabus, Spring 2010 (updated Feb 7, 2010.  Subject to revision)

Legged locomotion of robots and animals (a 5000 level course)
(aka TAM 7960, Mechanics of terrestrial locomotion)

Course home, Homework (pdf), References

Jan  26

Logistics. Introduction (legs, robots, animals).  Three ways to evaluate locomotion: 1) Effectiveness of motion (speed, versatility, appearance), 2) Energy of motion (e.g., VO2, COT), 3) Stability of motion (e.g., eigenvalues, basin of attraction, disturbance rejection). Three approaches: a) no control (passive dynamics), b) perfect control (optimization), c) details of how to do control.
Jan  28 Properties of motors and muscles.  Intro to electric motor equations.
Feb 2 Electric motors (cont'd)
Feb 4 Electric motors (cont'd).  Hill's law for muscles and muscle energetics.  Basic properties of muscles.
Feb  9 Point mass models. F=ma.  Basic energetics. `External Work' and its measurement.  Energetics of collisions.
Feb   11 Simple collisional models for the energetics of  dragging, hopping, running and walking.
Feb   16 General point-mass collision model for energetics of locomotion, including simultaneous collisions.  Springs (tendons).
Feb 18 Consequences of the general model for walking, running and galloping. Walking is subtle.
Feb 23 Point-mass model for brachiation. Spring-mass model for running.
Feb 25 Rigid-object models. Review of 2D mechanics. Matlab ODEs and animation.  Pendulum animation.
Mar 2 Rimless-wheel model of walking: ODEs, collisions and energetics.  Periodic motions.
Mar 4 The simplest walker (2-link passive model):  ODEs, collisions, simulation. 
Mar 9 Limit cycles, root finding,  stability and eigenvalues.
Mar 11 Stability of point-mass spring-mass models.
Mar 16 Raibert hopping robots: how they are controlled, simulation and stability.
Mar 18 Intro to Complex multi-object models of locomotion. Equations of motion.  Collisions.
Mar 30 How to calculate work and energy? Exact calculations. Approximate calculations.
Apr 1 Motor and muscle work vs Energy used.  Indirect calorimetry and VO2, metabolism, friction and resistive losses.
Apr 6 Biomechanics estimates and mis-estimates of work: 'external work', 'internal work', 'combined limbs' method, 'individual limbs' method.
Apr 8 Stability and energetics of complex models.
Apr 13 Energy optimality in locomotion. Predictive hypothesis? Useful for robot design? Intro to optimal control.
Apr 15 Evidence in favor and against energy optimality as a predictive hypothesis for animal locomotion.
Apr 20 Predictive theories of animal locomotion and generative theories of robot control. 1) passive dynamics, 2) optimality, 3) ZMP, linearized control of (non-linear) limit cycles...
Apr 22  ... predictive theories cont'd
Apr 27 Miscellaneous topics depending on class interest:  The African women paradox, the use of arms and upper body in human locomotion, reduced gravity locomotion, 4 legs vs 2, Cockroaches, Mechanics of pedaling, mechanics of rowing, ...
Apr 29 ...misc. topics cont'd...
May 4 ...misc. topics cont'd...
May 6 Summary and review.