This is an outline summary of our course schedule, which will be updated as the course progresses. 

 Dates TopicsSubtopics or Paper Titles Readings or Presenters Homework
31-Aug Introduction and Overview

 Overview of locomotion; review of matrix algebra  
2-Sep Configuration spaces I

 Manifolds and Lie groups (homeomorphisms, diffeomorphisms, direct products, isomorphisms) 1.1-1.2 
7-Sep Holiday - No class

9-Sep Geometry in locomotion

 Symmetries in Motion: Geometric Foundations of Motion Control (J. E. Marsden and J. Ostrowski) Matt Travers HW 0 assigned
14-Sep Configuration spaces I cont.

16-Sep Configuration spaces II; Velocity I

 Rigid bodies (semi-direct products); Tangent spaces and vector spaces 1.3, 2.1 HW 0 due
 HW 1 assigned
21-Sep Velocity II

 Tangent spaces and groupwise velocity (vector fields, Lie algebras, differential mappings) 2.1-2.2 
23-Sep Curvature and geodesics

 Geodesics and the exponential map
28-Sep Exponential maps

 Exponential maps, Lie groups, and Lie algebras   
30-Sep Forward kinematics I

 Fixed base arms and mobile articulated systems (holonomic constraints, kinematic terminology, generalized body frames)  3.1-3.4 HW 1 due
 HW 2 assigned
5-Oct Forward kinematics II

 Rigid body velocities, velocity kinematics (Jacobians) 3.5 
7-Oct Forward kinematics III Velocity kinematics (Jacobians), mobile articulated system velocities

12-Oct Kinematic locomotion I Shape space motion planning, modal shapes

14-Oct Kinematic locomotion II Fundamentals of kinematic locomotion (linearity, symmetry, nonholonomic constraints); full body locomotion (Pfaffian constraints and covectors)

 4.1-4.4 HW 2 due
 HW 3 assigned
19-Oct Kinematic locomotion III

 Geometric Motion Planning Analysis for Two Classes of Underactuated Mechanical Systems (E. Shammas et al.), Sect 1-6
 Akshara, Venkat, Arun 
21-Oct Gaits I On Reorienting Linked Rigid Bodies Using Internal Motions (G. Walsh and S. Sastry)

 Saiprasad, Elena, Hesham 
26-Oct Gaits II

 Satellite turning (nonconservativity and Stokes' theorem), parallel parking (noncommutativity and Lie brackets), undulatory locomotion, Hodge-Helmholtz decomposition

28-Oct Gaits III

 Nonconservativity and Noncommutativity in Locomotion (R. Hatton and H. Choset) Howie HW 3 due
 HW 4 assigned
2-Nov Dynamic systems
 Nonholonomic Mechanics and Locomotion: The Snakeboard Example (J. Ostrowski et al.)

 Ky, Roberto, Avinash 
4-Nov Dissipative systems Snakeboard Motion Planning with Viscous Friction and Skidding (T. Dear et al.)

 Brian, Quan 
9-Nov Projects
 Project spotlight presentations
11-Nov Projects
 Individual group meetings


 Ideal fluid dynamics Geometric Mechanics, Dynamics, and Control of Fishlike Swimming in a Planar Ideal Fluid (S. D. Kelly et al.) Ayush, Abhishek, Rohit HW 4 due
 HW 5 assigned
18-Nov Swimming Motion Planning for an Articulated Body in a Perfect Planar Fluid (J. B. Melli et al.) Katherine, Preeti, Goufan  
23-Nov No class 

25-Nov No class

30-Nov Biological locomotion Geometric Visualization of Self-Propulsion in a Complex Medium (R. L. Hatton et al.)
 Limbless Locomotors that Turn in Place (C. Gong et al.)

 Ziyang, Richard, Julian HW 5 due
2-Dec Project presentations

 Project presentations 
  7-Dec Project presentations

  9-Dec Project presentations