Set based velocity shaping for robotic manipulators

TL;DR

This paper introduces a novel framework for trajectory planning and safe state-feedback control of N-link robotic manipulators, enabling scalable, real-time implementation while ensuring adherence to environment constraints.

Contribution

It develops analytic algorithms for trajectory recovery and characterizes families of safe feedback controllers using a state feedback template, improving over previous open-loop methods.

Findings

Efficient online implementation demonstrated on a commercial robot.

Scalable algorithms for manipulators with multiple links.

Framework ensures safety and constraint adherence in real-time.

Abstract

We develop a new framework for trajectory planning on predefined paths, for general N-link manipulators. Different from previous approaches generating open-loop minimum time controllers or pre-tuned motion profiles by time-scaling, we establish analytic algorithms that recover all initial conditions that can be driven to the desirable target set while adhering to environment constraints. More technologically relevant, we characterise families of corresponding safe state-feedback controllers with several desirable properties. A key enabler in our framework is the introduction of a state feedback template, that induces ordering properties between trajectories of the resulting closed-loop system. The proposed structure allows working on the nonlinear system directly in both the analysis and synthesis problems. Both offline computations and online implementation are scalable with respect to the number of links of the manipulator. The results can potentially be used in a series of challenging problems: Numerical experiments on a commercial robotic manipulator demonstrate that efficient online implementation is possible.