Fast Swing-Up Trajectory Optimization for a Spherical Pendulum on a 7-DoF Collaborative Robot

Abstract

In this paper, the experimental swing-up of a spherical pendulum mounted on a collaborative robot is presented. The complete mechanical system consists of nine degrees of freedom (DoFs). The primary focus of this work is the design of a fast trajectory planning for the swing-up by systematically incorporating the kinematic and dynamics constraints. The proposed algorithm consists of two steps: First, an offline trajectory optimization is used to build a database of swing-up trajectories, with an average computing time of 10 s for one trajectory. Second, a fast trajectory replanner based on a constrained quadratic program is described, which computes the swing-up trajectory for an arbitrary initial configuration of the system with an average computing time of 0.2 s. Simulations and experimental results demonstrate the swing-up of the spherical pendulum using a discrete time-variant linear quadratic regulator as a feedback controller.