ABSTRACT
For the snakeboard example, steering comes from controlling φ as it affects the term I -1 = (—J /2, 0, Jtan</>/2)T. To see how the steering algo rithm could be implemented, we provide in Figure 6 a sample plot of motion control for the snakeboard mov ing from (x ,y , Θ) = (0, 0, 0) to (0, -5 .0 , π), along with a plot of the momentum as a function of time. Notice that in this plot the system first builds up momentum using a serpentine-like snakeboard “drive” gait in Step 1, and then executes a turn, a straight coast, and a final turn in Step 2. The turns are executed at the minimum turning radius, which we have constrained to be φγηαχ = ±1.0rad. For this simulation, we exe cute the same set of input motions at the end of the trajectory as was used at the start, except that the wheel angles are turned through opposite rotations of those used originally. These in-phase cyclic gaits used to build up and to reduce momentum at the start and finish of the motion are run for the same length of time. As is clear from the the right-hand graph in Figure 6, this results in a near exact cancelation of the momen tum that was built up during the initial motions.
