Multipoint boundary-value solution of two-point boundary-value problems
Journal of Optimization Theory and Applications
A multiple-shooting technique for optimal control
Journal of Optimization Theory and Applications
Collocation Software for Boundary-Value ODEs
ACM Transactions on Mathematical Software (TOMS)
Minimum-Energy Translational Trajectory Generation for Differential-Driven Wheeled Mobile Robots
Journal of Intelligent and Robotic Systems
A continuation/GMRES method for fast computation of nonlinear receding horizon control
Automatica (Journal of IFAC)
Hi-index | 22.14 |
This paper considers a nonlinear constrained optimal control problem (NCOCP) originated from energy optimal trajectory planning of servomotor systems. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. This paper proposes a method to manage the switching cost function to establish a set of necessary conditions of an NCOCP. Specifically, a concept ''sub-trajectory'' is introduced to match multiple Hamiltonian due to switches in the cost function. Necessary conditions on the optimal trajectory are established as a union of conditions for all sub-trajectories and Weierstrass-Erdmann corner conditions between sub-trajectories. The set of feasible structures of optimal trajectories is further identified and represented by various state transition diagrams for the servomotor application. A decomposition-based shooting method is proposed to compute an optimal trajectory by solving multi-point boundary value problems. Simulations and experiments validate the effectiveness of the methodology and the energy saving benefit.