Optimal Control for Time and Energy Minimization in the Trajectory Generation of a Mobile Robot

Trajectory generation for the point to point motion of wheeled mobile robots can be obtained using different approaches, usually with a pure geometric focus and classical controllers at the low or high level, with Cartesian coordinates or some specific coordinate transformations. Most of these approaches only consider the geometric path, without providing specific constraints on the robot energy or on the time it takes to move from the initial point to the goal. This paper presents a numeric optimal control approach that takes into account the minimization of energy as well as the final time optimization, while using the nonlinear robot kinematics throughout the motion. This approach is directly derived from the optimality conditions, turning the optimal control problem into a boundary value problem that can be solved with state-of-the-art numeric solvers. The fast computation of the undertaken approach can be used to recompute the trajectory online, acting like an MPC that indirectly closes the feedback loop. The approach has been tested in different configurations and the results show the successful application on a non-holonomic robotic structure.