Advances in Multi-Robot Path Planning and Singularity Avoidance in Single DOF Systems

Date of Award

12-1-2023

Degree Name

M.S. in Mechanical Engineering

Department

Department of Mechanical and Aerospace Engineering.

Advisor/Chair

Advisor: Andrew Murray

Abstract

This thesis presents the research that has been done in advancing topics in multi-robot coordinated path planning and singularity avoidance of mechanisms. For coordinated robots, an offline path planning solution has been developed that incorporates manufacturing constraints while taking into account the manipulator's kinematics and collision constraints. A loading dock optimization problem is first tackled due to it being a simpler system with one degree of freedom (DOF) while keeping the collaborative nature intact. Then the focus is shifted to spatial robots having 3 prismatic and/or revolute joints. This includes a discussion on the kinematics of the robots, the task allocation using a Tabu-Search Heuristic, and collision avoidance routines. The 3P robots have a one-to-one inverse kinematic solution with a unique configuration for any point within the workspace. This allows for a less computationally expensive optimization model. Finally, the path planning solution is applied to N overlapping 5R robots that have increased computational complexity due to one-to-many inverse kinematic solutions. As the number of links of the robot increases, the effort for combinatory collision checking routine explodes. Several simulations are presented to validate the proposed methodology. The research on singularity avoidance focuses on finding an actuating chain that can be attached to a mechanism to drive it in a singularity-free manner. For a single degree of freedom spatial mechanism, a reference frame attached to any of its links produces a continuous motion of this frame. Given the progression of this frame from the start through the end of the mechanism's motion, this research seeks to identify specific points relative to this moving reference frame. The points of interest are those that can be coupled with a second point determined in the fixed frame to act as the end joint locations for a spherical-prismatic-spherical (SPS) driving chain. If the selection of the point pair is made such that the change in distance between them as the mechanism moves is strictly monotonic, then the SPS chain they define is potentially capable of driving the mechanism over the desired range of motion. This motion is referred to as locally P-drivable because a global solution is not ensured by the process proposed herein. This synthesis process can avoid singularities encountered by actuating the mechanism at one of its original joints. The proposed approach enables the dimensional synthesis of a single degree-of-freedom mechanism to focus on creating circuit-defect-free solutions without concern for potential singular positions. The actuating chain can then be determined as a separate step in the synthesis process. This research also considers motions that are not P-drivable and the specialization to planar systems with the synthesis of a P-drivable RPR chain.

Keywords

Multi-robot Path Planning, Robotic Task Sequencing Problem, Robotic Collision Avoidance, Singularity-free actuation, Spatial Mechanism Synthesis, Coupler-Driven Linkage

Rights Statement

Copyright © 2023, author.

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