A Parameter-Linear Formulation of the Optimal Path Following Problem for Robotic Manipulator

TL;DR

This paper introduces a novel, computationally efficient method for time-optimal path following in robotic manipulators by maximizing path speed and reformulating the problem as a linear optimization, avoiding singularities.

Contribution

It presents a parameter-linear reformulation of the path following problem that enables smooth trajectory planning without singularities and with low computational effort.

Findings

The approach is capable of planning smooth trajectories efficiently.

The reformulation is linear in optimization variables.

The method avoids singularities at zero path speed.

Abstract

In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization problem in terms of a path parameter. Thus, smooth trajectory generation while maintaining a low computational effort is quite challenging, since the singularities have to be taken into account. To this end, a different approach is presented in this paper. This approach is based on maximizing the path speed along a prescribed path. Furthermore, the approach is capable of planning smooth trajectories numerically efficient. Moreover, the discrete reformulation of the underlying problem is linear in optimization variables.