Optimal path planning of two-wheeled mobile robots in the presence of dynamic obstacles

To solve the problem of optimal path planning of two-wheeled mobile robots (TWMRs) in the presence of dynamic obstacles, a symplectic pseudospectral method for solving nonlinear optimal control problems with inequality constraints is developed. The proposed algorithm transforms the original nonlinear optimal problem into a series of linear-quadratic optimal control problems (LQOCPs) by using quasilinearization techniques. And the LQOCP in each iteration is replaced by a coupling of a system of linear algebraic equations and a linear complementarity problem (LCP) with the help of the parametric variational principle and the second kind of generating function. The proposed method satisfies the first-order necessary conditions for optimal control problems and matrices involved are found to be sparse and symmetric, leading it to be accurate and efficient. Numerical simulations demonstrate that the proposed method is effective for nonlinear optimal control problems with complicated constraints.