Non-Holonomic Motion Planning with PSO and Spline Approximation

An optimal motion planning scheme using a modified particle swarm optimization (PSO) is proposed for non-holonomic systems. A cost function is used to incorporate the final errors and control energy. The motion planning is to determine control inputs to minimize the cost function and is formulated as an infinite dimensional optimal control problem. By using the control parameterization, the infinite dimensional optimal control problem can be transformed to a finite dimensional one. A Hybrid PSO algorithm with mutation is presented to resolve the finite dimension optimal control problem. The cubic spline approximation is introduced to realize the control parameterization. The resulting controls are smoother and the initial values of the resulting controls are zeros, so they are easily generated by servomotors. Simulations are also performed for the non-holonomic motion planning of a unicycle mobile robot. Experimental results show that the proposed algorithm is more effective than the Newton algorithm.