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

Abstract

In this paper, the problem of time optimal trajectory planning under confined torque and uncertain dynamics and torque parameters along a predefined geometric path is considered. It is shown that the robust optimal solution to such a problem can be obtained by solving a linear program. Thus a tractable algorithm is given for robust time-optimal path-tracking control under confined torque.

An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation

“…A three-DOF elbow manipulator with a basic link and two arms 6,12,16 is used to illustrate the validity of the proposed approach in Fig. 2.…”

“…In the general case, due to the special structure of the problem, the method gives challenges for efficient numerical solution. In the recent work, 12 the min-max optimal trajectory planning problem under limited actuation is converted to a min-max linear optimization problem which in turn can be reduced to a linear programming problem. Methods were proposed to treat uncertainties under certain special distributions.…”

“…[9,15] to treat the probabilistic inequality fails. In comparison with robust method, 12 where the solutions obtained are near optimal, our new method reduces the problem to an equivalent linear optimal control problem and obtains the optimal solutions. Besides, it solves the problem more quickly since it does not add redundant variables.…”

Practical feedrate optimization for planar high precision contouring

“…From Zhang et al [12], we have the fact that the optimal solution of the normal P is unique and is maximum among all feasible solutions for any u ∈ [0, 1]. So let q o (u) be any feasible solution of problem (11)- (14) which is also feasible for the normal P , then we always have…”

“…(12), (14) and (26) of the feedrate planning problem can be reconstructed to a second order cone programming (SOCP) problem, which can be solved efficiently since there exist polynomial complexity SOCP algorithms [14].…”