Time Optimal Path Planning for Industrial Robots: A Dynamic Programming Approach Considering Torque Derivative and Jerk Constraints

Abstract

This paper presents a dynamic programming approach for calculating time optimal trajectories for industrial robots, subject to various physical constraints. In addition to path velocity, motor torque, joint velocity and acceleration constraints, the present contribution also shows how to deal with torque derivative and joint jerk limitations. First a Cartesian path for the endeffector is defined by splines using Bernstein polynomials as basis functions and is parameterized via a scalar path parameter. In order to compute the belonging quantities in configuration space, inverse kinematics is solved numerically. Using this and in combination with the dynamical model, joint torques as well as their derivatives can be constrained. For that purpose the equations of motion are calculated with the help of the Projection Equation. As a consequence of the used optimization problem formulation, the dynamical model as well as the restrictions have to be transformed to path parameter space. Due to the additional consideration of jerk and torque derivative constraints, the phase plane is expanded to a phase space. The parameterized restrictions lead to feasible regions in this space, in which the optimal solution is sought. Result of the optimization is the time behavior of the path parameter and subsequently the feed forward torques for the optimal motion on the spatial path defined by previously mentioned splines. Simulation results as well as experimental results for a three axes industrial robot are presented.

Successive dynamic programming and subsequent spline optimization for smooth time optimal robot path tracking

“…Smooth trajectories can be achieved by taking jerk or torque rate restrictions into account. In Constantinescu and Croft (2000) and Oberherber et al (2014) methods to consider them in phase space are presented, while Debrouwere et al (2013) proposes a sequential convex scheme to solve a nonlinear program. However, for standard six axis industrial robots and long geometric paths the calculation effort is enormous due to the high number of optimization variables and restrictions.…”