Convex Optimization approach for Time-Optimal Path Tracking of Robots with Speed Dependent Constraints

Abstract

The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive system. It is shown how the speed dependent constraints should be added in order to keep the convexity of the overall problem. A method to, conservatively, approximate the linear speed dependent constraints by a convex constraint is also proposed. A numerical example proves versatility of the extension proposed in this paper.

A Dynamic Programming Approach for Time‐Optimal Path Following of Robots Considering Speed Dependent Torque Constraints

“…For this reason velocity limitsq have to be chosen, causing an unexploited potential. In [4] torque constraints are approximated with affine functions to consider them within a convex optimization. In contrast to this, we use the constraints provided by data sheets directly within a DP approach [5].…”

Path Tracking Algorithms for Non-Convex Waiter Motion Problem

“…As an alternative to direct approach, the motion planning problem is often decoupled [2,3]. First, a high-level geometry path planner determines a path for the robot considering geometric constraints and ignoring system dynamics.…”

“…Direct approaches [1] or one step methods solve the entire problem in one step. In general it is a highly difficult task, since both the geometric constraints (including collision avoidance), and the timing along this geometric path (including dynamic limitation) have to be optimized.As an alternative to direct approach, the motion planning problem is often decoupled [2,3]. First, a high-level geometry path planner determines a path for the robot considering geometric constraints and ignoring system dynamics.…”

Tractable Algorithm for Robust Time-Optimal Trajectory Planning of Robotic Manipulators under Confined Torque

“…Many efficient approaches for the time minimum trajectory planning (TMTP) problem along a predefined geometric path have been proposed, including the phase plane analysis approaches [3][4][5][6], the Pontryagin maximum principle and shooting algorithms [7], the convex optimization [2,10], the path reshaping [8], and the direct search method [9]. The recent works [2,11] are significant in which general and efficient methods are proposed.…”