A nonlinear least squares approach to the numerical optimal control of non-holonomic systems

This paper gives a nonlinear least squares approach for numerically finding a trajectory to transfer a non-holonomic system from one configuration to another while satisfying given point-wise configuration constraints. A car-like robot is considered as an example. The car-like robot is kinematically constrained and is modelled as a 2D object translating and rotating in the horizontal plane. The configuration constraints correspond to obstacle-avoidance. A simple technique is used to set up an approximate nonlinear least squares problem that includes the various constraints. An elegant error analysis is devised to effectively deal with the approximations. Several illustrative examples are presented to demonstrate the effectiveness of the approach