Path Planning and Control of Redundant Manipulators Using Bilevel Optimization

Redundancy is a useful feature in dynamic systems which can be exploited to enhance performance in various tasks. In this work, redundancy will be utilized to minimize the energy consumption of a linear manipulator, while in some cases an additional task of end-effector tracking will also be required and achieved. Optimal control theory has been extensively used for the optimization of dynamic systems; however, complex tasks and redundancy make these problems computationally expensive, numerically difficult to solve, and in many cases, ill-defined. In this paper, evolutionary bilevel optimization for the problem is presented. This is done by setting up an upper level optimization problem for a set of decision variables and a lower level one that actually calculates the optimal inputs and trajectories. The upper level problem is solved by a genetic algorithm (GA), whereas the lower level problem uses classical optimal control. As a result, the proposed algorithm allows the optimization of complex tasks that usually cannot be solved in practice using standard optimal control tools. In addition, despite the use of penalty functions to enforce saturation constraints, the algorithm leads to global energy minimization. Illustrative examples of a redundant x-y robotic manipulator with complex overall tasks will be presented, solved, and discussed.