Self-Tuning Time-Energy Optimization for the Trajectory Planning of a Wheeled Mobile Robot

In this work a method for trajectory planning based on time-energy optimization of a nonholonomic wheeled mobile robot is proposed. The method utilizes a nonlinear variable change that transforms the nonlinear optimization problem into a discrete second order cone programming that can be solved by convex optimization tools. The formulation of the multiobjective function has two components: the total energy and the traversal time that is weighted by a parameter named penalty coefficient. With the use of the penalty coefficient one can establish a trade-off between the optimization of the total energy and the traversal time. The relation between both objectives draws a Pareto Front in the criterion space parameterized by the penalty coefficient. The rationale of this paper is to assume that the Pareto curve is an exponential function, and to propose an algorithm to estimate its parameters. Using this exponential function it is possible to estimate the Knee Point that is an optimal solution that balances time and energy equally. This systematic approach might be understood as a self-tuning algorithm that estimate the penalty coefficient for the generation of optimal voltage signals. Numerical results illustrate the feasibility of the proposed method.