We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation analysis and the design of inversion primitives and composition methods. We illustrate the algorithms on an underactuated planar rigid body and on a satellite with two thrusters.
|Journal||IEEE Transactions on Automatic Control|
|Publication status||Published - Dec 2008|
- Mechanical systems
- underactuated systems
- relative equilibria
- nonlinear control