Joint Exploration of Local Metrics and Geometry in Sampling-based Planning

This thesis addresses how the local geometry of the workspace around a system state can be combined with local metrics describing system dynamics to improve the connectivity of the graph produced by a sampling-based planner over a fixed number of configurations. This development is achieved through generalization of the concept of the local free space to inner products other than the Euclidean inner product. This new structure allows for naturally combining the local free space construction with a locally applicable metric. The combination of the local free space with two specific metrics is explored in this work. The first metric is the quadratic cost-to-go function defined by a linear quadratic regulator, which captures the local behavior of the dynamical system. The second metric is the Mahalanobis distance for a belief state in a belief space planner. Belief space planners reason over distributions of states, called belief states, to include modeled uncertainty in the planning process. The Mahalanobis distances metric for a given belief state can be exploited to include notions of risk in local free space construction. Numerical simulations are provided to demonstrate the improved connectivity of the graph generated by a sampling-based planner using these concepts

Sampling-Based Motion Planning: A Comparative Review

Sampling-based motion planning is one of the fundamental paradigms to generate robot motions, and a cornerstone of robotics research. This comparative review provides an up-to-date guideline and reference manual for the use of sampling-based motion planning algorithms. This includes a history of motion planning, an overview about the most successful planners, and a discussion on their properties. It is also shown how planners can handle special cases and how extensions of motion planning can be accommodated. To put sampling-based motion planning into a larger context, a discussion of alternative motion generation frameworks is presented which highlights their respective differences to sampling-based motion planning. Finally, a set of sampling-based motion planners are compared on 24 challenging planning problems. This evaluation gives insights into which planners perform well in which situations and where future research would be required. This comparative review thereby provides not only a useful reference manual for researchers in the field, but also a guideline for practitioners to make informed algorithmic decisions.Comment: 25 pages, 7 figures, Accepted for Volume 7 (2024) of the Annual Review of Control, Robotics, and Autonomous System

Chance-Constrained Multi-Robot Motion Planning under Gaussian Uncertainties

We consider a chance-constrained multi-robot motion planning problem in the presence of Gaussian motion and sensor noise. Our proposed algorithm, CC-K-CBS, leverages the scalability of kinodynamic conflict-based search (K-CBS) in conjunction with the efficiency of the Gaussian belief trees used in the Belief-A framework, and inherits the completeness guarantees of Belief-A's low-level sampling-based planner. We also develop three different methods for robot-robot probabilistic collision checking, which trade off computation with accuracy. Our algorithm generates motion plans driving each robot from its initial state to its goal while accounting for the evolution of its uncertainty with chance-constrained safety guarantees. Benchmarks compare computation time to conservatism of the collision checkers, in addition to characterizing the performance of the planner as a whole. Results show that CC-K-CBS can scale up to 30 robots.Comment: Submitted to 2023 IEEE International Conference on Intelligent Robots and Systems (IROS