Experimental and Novel Analytical Trajectory Optimization of a 7-DOF Baxter Robot: Global Design Sensitivity and Step Size Analyses

Abstract

In this paper, we present a novel nonlinear analytical coupled trajectory optimization of a 7-DOF Baxter manipulator validated through experimental work utilizing global optimization tools. The robotic manipulators used in network-based applications of industrial units and even homes, for disabled patients, spend significant lumped amount of energy and therefore, optimal trajectories need to be generated to address efficiency issues. We here examine both heuristic (Genetics) and gradient based (GlobalSearch) algorithms for a novel approach of “S-Shaped” trajectory (unlike conventional polynomials), to avoid being trapped in several possible local minima along with yielding minimal computational cost, enforcing operational time and torque saturation constraints. The global schemes are utilized in minimizing the lumped amount of energy consumed in a nominal path given in the collision-free joint space except an impact between the robot’s end effector and a target object for the nominal operation. Note that such robots are typically operated for thousands of cycles resulting in a considerable cost of operation. Due to the expected computational cost of such global optimization algorithms, step size analysis is carried out to minimize both the computational cost (iteration) and possibly cost function by finding an optimal step size. Global design sensitivity analysis is also performed to examine the effects of changes of optimization variables on the cost function defined.

Multivariable Extremum Seeking for Joint-Space Trajectory Optimization of a High-Degrees-of-Freedom Robot

“…Also, MðqÞ 2 R 7Â7 ; Cðq; _ qÞ 2 R 7Â7 , and /ðqÞ 2 R 7 are the mass, Coriolis, and gravitational matrices, respectively. This coupled nonlinear dynamic model of the robot is used in the optimization process [43,44].…”

Perfect Torque Compensation of Planar 5R Parallel Robot in Point-to-Point Motions, Optimal Control Approach

“…The cost function is formulated as mechanical energy consumption with torque saturation constraints. 15 Gong et al performed a study on the optimal control to find optimal pose at target for a planar 3-DOF manipulator. Accordingly, they reached an optimal trajectory for which the torque was minimized while dynamics were taken into consideration.…”