Optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation

An optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems. The motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system. A cost function is introduced to incorporate the control energy and the final state errors. The control inputs are determined to minimize the cost functional. By using the method of wavelet, the infinite-dimensional optimal control problem is truncated to a finite-dimensional one based on the wavelet bases. The genetic algorithm is employed to solve a feasible trajectory satisfying nonholonomic constraints. The proposed scheme is applied to a free-floating robot consisting of two one-link arms connected to a main base via revolute joints. The numerical results demonstrate that the genetic algorithm with the wavelet approximation is an effective approach to steer a nonholonomic system from its initial state to its final state.