(aka TAM 7960, Mechanics of terrestrial locomotion)

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. |