Reachability based planning for robotic manipulators

Abstract

In the domain of modern robotics there still exist challenges in control on arguably one of the most fundamental levels, that is motion control. Since the 1980s there has been research into how to take advantage of the system dynamics of robots to provide better methods for motion control. In this thesis we explore the problem of providing control strategies to produce motions on robots, with formal guarantees of safety. In the context of this thesis a robot refers to an N link, serial robotic manipulator, and \emph{safety} implies the chosen a constraint set for a motion must be respected for all states the system takes.

Inspired by the line of seminal works on projected path dynamics and time optimal control of robots which originated in the eighties, and recent advances on the computation of safe sets for complex systems in control, we present a new trajectory planning framework for N-link robotic manipulators. Given a path, defined typically in the workspace, we recover the admissible velocity profiles and the realisable corresponding torque profiles that achieve a path traversal. To make this possible, we introduce a new torque feedback parameterisation. This enables us to construct the set where the trajectory of the projected path can be confined while reaching a target set with a feasible control action, namely, the reach-avoid set. As a product of this procedure, we develop feedback controllers that guarantee state and input constraint satisfaction, can track reference trajectories, and can handle temporal specifications related, for example, to rendezvous and avoidance setups. Encouraging experimental evaluation of our theoretical results on a UR10 robotic manipulator suggests the framework and extensive simulation toolbox can complement and further expand the existing classical approaches.

We extend trajectory planning methods for robotic manipulators to the more general and complex path planning problem in both the space of joints and their velocities. We consider a set of prespecified feasible paths, together with their associated, precomputed safe sets in the projected space of the dynamics restricted to the path. We ask a natural question, namely, whether we can state geometric conditions, together with their algebraic equivalents, that allow switching between paths, providing thus greater flexibility, enabling path planning capabilities. We answer affirmatively, and pose conditions whose consistency can be checked by solving a set of algebraic conditions and by computing intersections between safe sets, precisely, reach-avoid sets. Controllers can also be extracted for closed-loop switched paths. Our proof-of-concept analysis suggests that under the developed framework, composition between paths is possible, thus, potentially significantly extending the applicability of the approach and complementing existing planning methods.

Date of Award	Dec 2024
Original language	English
Awarding Institution	Queen's University Belfast
Sponsors	Northern Ireland Department for the Economy
Supervisor	Seán McLoone (Supervisor) & Nikolaos Athanasopoulos (Supervisor)