A minimum swept-volume metric structure for configuration space

Borrowing elementary ideas from solid mechanics and differential geometry, this presentation shows that the volume swept by a regular solid undergoing a wide class of volume-preserving deformations induces a rather natural metric structure with well-defined and computable geodesics on its configuration space. This general result applies to concrete classes of articulated objects such as robot manipulators, and we demonstrate as a proof of concept the computation of geodesic paths for a free flying rod and planar robotic arms as well as their use in path planning with many obstacles

Reachability-based Trajectory Design with Neural Implicit Safety Constraints

Generating safe motion plans in real-time is a key requirement for deploying robot manipulators to assist humans in collaborative settings. In particular, robots must satisfy strict safety requirements to avoid self-damage or harming nearby humans. Satisfying these requirements is particularly challenging if the robot must also operate in real-time to adjust to changes in its environment.This paper addresses these challenges by proposing Reachability-based Signed Distance Functions (RDFs) as a neural implicit representation for robot safety. RDF, which can be constructed using supervised learning in a tractable fashion, accurately predicts the distance between the swept volume of a robot arm and an obstacle. RDF's inference and gradient computations are fast and scale linearly with the dimension of the system; these features enable its use within a novel real-time trajectory planning framework as a continuous-time collision-avoidance constraint. The planning method using RDF is compared to a variety of state-of-the-art techniques and is demonstrated to successfully solve challenging motion planning tasks for high-dimensional systems faster and more reliably than all tested methods

OOPS for Motion Planning: An Online Open-source Programming System

Abstract — The success of sampling-based motion planners has resulted in a plethora of methods for improving planning components, such as sampling and connection strategies, local planners and collision checking primitives. Although this rapid progress indicates the importance of the motion planning problem and the maturity of the field, it also makes the evaluation of new methods time consuming. We propose that a systems approach is needed for the development and the experimental validation of new motion planners and/or components in existing motion planners. In this paper, we present the Online, Open-source, Programming System for Motion Planning (OOPSMP), a programming infrastructure that provides implementations of various existing algorithms in a modular, object-oriented fashion that is easily extendible. The system is open-source, since a community-based effort better facilitates the development of a common infrastructure and is less prone to errors. We hope that researchers will contribute their optimized implementations of their methods and thus improve the quality of the code available for use. A dynamic web interface and a dynamic linking architecture at the programming level allows users to easily add new planning components, algorithms, benchmarks, and experiment with different parameters. The system allows the direct comparison of new contributions with existing approaches on the same hardware and programming infrastructure. I

Computational Frameworks for Multi-Robot Cooperative 3D Printing and Planning

This dissertation proposes a novel cooperative 3D printing (C3DP) approach for multi-robot additive manufacturing (AM) and presents scheduling and planning strategies that enable multi-robot cooperation in the manufacturing environment. C3DP is the first step towards achieving the overarching goal of swarm manufacturing (SM). SM is a paradigm for distributed manufacturing that envisions networks of micro-factories, each of which employs thousands of mobile robots that can manufacture different products on demand. SM breaks down the complicated supply chain used to deliver a product from a large production facility from one part of the world to another. Instead, it establishes a network of geographically distributed micro-factories that can manufacture the product at a smaller scale without increasing the cost. In C3DP, many printhead-carrying mobile robots work together to print a single part cooperatively. While it holds the promise to mitigate issues associated with gantry-based 3D printers, such as lack of scalability in print size and print speed, its realization is challenging because existing studies in the relevant literature do not address the fundamental issues in C3DP that stem from the amalgamation of the mobile nature of the robots, and continuous nature of the manufacturing tasks. To address this challenge, this dissertation asks two fundamental research questions: RQ1) How can the traditional 3D printing process be transformed to enable multi-robot cooperative AM? RQ2) How can cooperative manufacturing planning be realized in the presence of inherent uncertainties in AM and constraints that are dynamic in both space and time? To answer RQ1, we discretize the process of 3D printing into multiple stages. These stages include chunking (dividing a part into smaller chunks), scheduling (assigning chunks to robots and generating print sequences), and path and motion planning. To test the viability of the approach, we conducted a study on the tensile strength of chunk-based parts to examine their mechanical integrity. The study demonstrates that the chunk-based part can be as strong as the conventionally 3D-printed part. Next, we present different computational frameworks to address scheduling issues in C3DP. These include the development of 1) the world-first working strategy for C3DP, 2) a framework for automatic print schedule generation, evaluation, and validation, and 3) a resource-constrained scheduling approach for C3DP that uses a meta-heuristic approach such as a modified Genetic Algorithm (MGA) and a new algorithm that uses a constraint-satisficing approach to obtain collision-free print schedules for C3DP. To answer RQ2, a multi-robot decentralized approach based on a simple set of rules is used to plan for C3DP. The approach is resilient to uncertainties such as variation in printing times and can even outperform the centralized approach that uses MGA with a conflict-based search for large-scale problems. By answering these two fundamental questions, the central objective of the research project to establish computational frameworks to enable multi-robot cooperative manufacturing was achieved. The search for answers to the RQs led to the development of novel concepts that can be used not only in C3DP, but many other manufacturing tasks, in general, requiring cooperation among multiple robots