Cooperative Manipulation and Motion Planning Under Signal Temporal Logic Specifications

QC 20230403

Abstract

As robots become increasingly prevalent in society, it is essential to prescribe complex high-level tasks to them. Tasks prescribed over temporal logics present two main challenges: generating trajectories that satisfy the logical formula and tracking those trajectories that depend on the logical formula. This thesis aims to address these challenges. Firstly, we use Prescribed Performance Control (PPC) to solve the cooperative manipulation problem based on constraints defined by an Signal Temporal Logic (STL) formula. Secondly, we design a planning algorithm that generates spatio-temporal trees and searches for trajectories that satisfy an STL formula for cooperating agents. Finally, we utilise gradient-based methods to shape trajectories that satisfy an STL formula for multiple cooperating agents. Our approach is based on integration of tools from the areas of multi-agent systems, optimisation theory, cooperative object manipulation and motion planning. More specifically, in the second chapter we start by focusing on solving the problem of cooperative manipulation of an object specified by an STL formula. To achieve this, we utilise the PPC methodology, which enforces the desired transient and steady-state performance on the object trajectory to satisfy the STL formula. Specifically, we propose a method that translates the problem of satisfying an STL task into the problem of state evolution within a custom-defined time-varying funnel, which is then used to design a decentralised control strategy for robotic agents. The strategy guarantees compliance with the funnel, and each agent calculates its own control signal, without utilising any information on the dynamic terms of the agents or object. We provide experimental validation of our approach using two manipulator arms cooperatively manipulating an object based on a specified STL formula. In the next chapter, we present a novel motion planning algorithm for two autonomous agents working together to accomplish coupled tasks expressed as STL constraints. The proposed algorithm is a cooperative sampling-based approach that builds two spatio-temporal trees incrementally, one for each agent. This is achieved by sampling points in an extended space, which is a compact subset of the time domain and physical space of the agents. The algorithm constructs the trees by checking if newly sampled points form edges in time and space that satisfy certain parts of the coupled task. As a result, the constructed trees represent time-varying trajectoriesin the agents’ state space that satisfy the task. The algorithm is distributed and inherits the properties of probabilistic completeness and computational efficiency from the original sampling-based procedures. And in the final chapter, we present a distributed algorithm that can generate continuous trajectories for multiagent systems based on an STL formula. The STL formula is designed over functions that are coupled to the states of neighbouringagents. The algorithm is distributed, meaning that each agent independently com-putes its own trajectory by only communicating with its immediate neighbours. The approach is verified through various simulated scenarios.

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