Trajectory Generation for a Multibody Robotic System using the Product of Exponentials Formulation

摘要

View Video Presentation: https://doi.org/10.2514/6.2021-2016.vid This paper presents a trajectory generation algorithm for multibody robotic systems based on the Product of Exponentials (PoE) formulation, also known as screw theory. A PoE formulation is first developed to model the kinematics and dynamics of a multibody robotic manipulator with 7 revolute joints and an end effector. An inverse kinematic algorithm based on the Newton-Raphson iterative method is then applied to generate constrained joint-space trajectories corresponding to straight-line motion of the end effector in Cartesian space with finite jerk. Derivatives of these joint-space trajectories are computed using Bézier curves, which ensures dynamically feasible trajectories. A novel method of Mean Arctangent Absolute Percentage Error (MAAPE) is then used to check accuracy of the derivatives of joint-space trajectories. The Newton-Euler recursive algorithm is then implemented to compute the inverse dynamics, which generates the joint torques required to achieve the reference trajectories. These torques are then incorporated into a closed-loop control algorithm, and simulation studies are performed using a dynamic model of the robotic system. The simulation results demonstrate that the proposed approach is able to successfully generate constrained trajectories, the MAAPE shows that lower order Bézier curves approximate the joint-space derivatives with the same accuracy as higher order polynomials, and the closed-loop controller provides accurate trajectory tracking subject to model uncertainties. This algorithm can be used to generate trajectories for robotic arms performing spacecraft servicing missions, because it also takes into account the variable gravity vector. The significant contribution of this method is integration of all of these techniques applied to a multibody robotic system.