Multi-objective Optimal Path Planning for Mobile Robots using State Space Cell Mapping

Cell mapping is a promising approach in multiple objective optimization problems. By discretizing the open-loop dynamical system in both the state space and time, it is possible to reduce the mathematical complexity of the problem while introducing constraints in practical mobile robots. Here, we propose to perform the discretization of the controlled system (closed-loop). This can be done introducing an additional constraint in the model that can be interpreted as a zero-order hold (ZOH) on the control. Because of the structure of the optimal problem, it is necessary to release a degree of freedom. This is achieved by allowing nonuniform discretization of time. We study the problem of a particle on a bidimensional configuration space with obstacles, optimizing time, distance and control energy. We also present some numerical results in a case of study with a three wheeled omnidirectional mobile robot in a constrained C-space.