Koichiro Ueda

On the optimal trajectory generation for servomotors: A Hamiltonian approach

This note considers the energy optimal trajectory generation of servo systems through open-loop optimal control design approach. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. The minimum principle is applied to establish piecewise necessary optimality conditions. An approximate optimal control is proposed to circumvent the difficulty due to the nonlinearity of the cost function. Simulation is performed to illustrate the generation of the approximate optimal trajectory.

Energy-Efficient Trajectory Planning for a Mobile Agent by Using a Two-Stage Decomposition Approach

Abstract This paper presents a new approach for the energy-efficient trajectory planning of a mobile agent with obstacle avoidance. The motion of the mobile agent is subject to position constraints characterizing an obstacle (keep-out region) as well as velocity, acceleration, and control constraints. The original optimal control problem is transformed into a mathematical programming problem where the obstacle is described by a set of linear constraints and switching times, which specify the sequence of active constraints corresponding to the obstacle. A two-stages decomposition method is proposed to solve the optimal control inputs and switch times and is verified through simulations. The proposed approach can be applied to solve general obstacle avoidance trajectory planning problems.