Minimum energy trajectory for an underwater manipulator and its simple planning method by using a Genetic Algorithm

Abstract

In this paper, a trajectory planning method for an underwater manipulator is proposed. whose criterion of path generation is the energy consumption during operation. The trajectory planning for an underwater manipulator is formulated as a nonlinear optimal control problem. The minimum energy trajectory is obtained as the solution of the two-point boundary-value problem. From the results of a series of numerical calculations, moving the manipulator (e.g. folding its arm) is effective to reduce energy consumption during motion. It is also clear that the optimal travel time of the motion exists when an unbalance of static forces, buoyancy and gravity forces, occurred by a payload and so on. Then to calculate the trajectory without the complexity of formulation and computation, a simple trajectory planning method is also proposed, which uses a Genetic Algorithm (GA). In this method, a polynomial approximates time histories of the trajectory in joint space; the GA determines the parameter of the polynomial to minimize the energy consumption. This method does not need a special formulation and can calculate the trajectory with less computation than the previous method. Enhancing the problem to the search for the optimal travel time is easy. From the results of the simulation. it is shown that the trajectory is obtained by this method, which is similar to that derived as the solution of the two-point boundary-value problem.