Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal. 
Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots