Joint-Space Trajectory Optimization of a 7-DOF Baxter Using Multivariable Extremum Seeking

In this paper, a novel analytical coupled trajectory optimization of a 7-DOF Baxter manipulator utilizing Extremum Seeking (ES) approach is presented. The robotic manipulators are used in network-based industrial units, and even homes, by expending a significant lumped amount of energy and therefore, optimal trajectories need to be generated to address efficiency issues. These robots are typically operated for thousands of cycles resulting in a considerable cost of operation. First, coupled dynamic equations are derived using the Lagrangian method and experimentally validated to examine the accuracy of the model. Then, global design sensitivity analysis is performed to investigate the effects of changes of optimization variables on the cost function leading to select the most effective ones. We examine a discrete-time multivariable gradient-based extremum seeking scheme enforcing operational time and torque saturation constraints in order to minimize the lumped amount of energy consumed in a path given. The results are compared with those of a global heuristic genetic algorithm to discuss the locality/globality of optimal solutions. Finally, the optimal trajectory is experimentally implemented to be thoroughly compared with the inefficient one. The results reveal that the proposed scheme yields the minimum energy consumption in addition to overcoming the robot's jerky motion observed in an inefficient path.