15.5.2 Using Sinusoidal Action Trajectories

The steering method presented in this section is based on initial work by Brockett [142] and a substantial generalization of it by Murray and Sastry [727]. The approach applies to several classes of systems for which the growth of independent vector fields occurs as quickly as possible. This means that when the P. Hall basis is constructed, no elements need to be removed due to linear dependency on previous Lie products or system vector fields. For these systems, the approach applies sinusoids of integrally related frequencies to some action variables. This changes some state variables while others are automatically fixed. For more details beyond the presentation here, see [596,725,727,846].

- 15.5.2.1 Steering the nonholonomic integrator
- 15.5.2.2 First-order controllable systems
- 15.5.2.3 Chained-form systems

Steven M LaValle 2012-04-20