Dynamic Obstacle Avoidance on a Self-balancing Robot Platform

Autonomous tasks are increasingly becoming part of our everyday life, whether in a factory floor where robotic manipulators manufacture goods, or when cars acquire the capability of parking themselves. These tasks often involve a human operator that has some high level control over the system. This can lead to situations where the human operator believes that the system is safe, when this might not be the case. This is why robust control algorithms need to be implemented that provide safety guarantees when a mechanical device is teleoperated by a human user. These algorithms can intervene when an unsafe choice is made to protect the operator and the system itself. The challenge that this work specifically focuses upon is dynamic obstacle avoidance by a robotic unit that is guided by a human user. Dynamic obstacles are objects that move in the environment independently from the robot and can potentially raise safety concerns for the robotic platform. In order to detect these obstacles in the environment, sensor data along with some probabilities need to be utilized to infer the magnitude and direction of an object’s speed. This project is primarily concerned with this estimation and methods to do this accurately

Probabilistic completeness of RRT for geometric and kinodynamic planning with forward propagation

The Rapidly-exploring Random Tree (RRT) algorithm has been one of the most prevalent and popular motion-planning techniques for two decades now. Surprisingly, in spite of its centrality, there has been an active debate under which conditions RRT is probabilistically complete. We provide two new proofs of probabilistic completeness (PC) of RRT with a reduced set of assumptions. The first one for the purely geometric setting, where we only require that the solution path has a certain clearance from the obstacles. For the kinodynamic case with forward propagation of random controls and duration, we only consider in addition mild Lipschitz-continuity conditions. These proofs fill a gap in the study of RRT itself. They also lay sound foundations for a variety of more recent and alternative sampling-based methods, whose PC property relies on that of RRT

Efficient and Asymptotically Optimal Kinodynamic Motion Planning

This dissertation explores properties of motion planners that build tree data structures in a robot’s state space. Sampling-based tree planners are especially useful for planning for systems with significant dynamics, due to the inherent forward search that is performed. This is in contrast to roadmap planners that require a steering local planner in order to make a graph containing multiple possible paths. This dissertation explores a family of motion planners for systems with significant dynamics, where a steering local planner may be computationally expensive or may not exist. These planners focus on providing practical path quality guarantees without prohibitive computational costs. These planners can be considered successors of each other, in that each subsequent algorithm addresses some drawback of its predecessor. The first algorithm, Sparse-RRT, addresses a drawback of the RRT method by considering path quality during the tree construction process. Sparse-RRT is proven to be probabilistically complete under mild conditions for the first time here, albeit with a poor convergence rate. The second algorithm presented, SST, provides probabilistic completeness and asymptotic near-optimality properties that are provable, but at the cost of additional algorithmic overhead. SST is shown to improve the convergence rate compared to Sparse-RRT. The third algorithm, DIRT, incorporates learned lessons from these two algorithms and their shortcomings, incorporates task space heuristics to further improve runtime performance, and simplifies the parameters to more user-friendly ones. DIRT is also shown to be probabilistically complete and asymptotically near-optimal. Application areas explored using this family of algorithms include evaluation of distance functions for planning in belief space, manipulation in cluttered environments, and locomotion planning for an icosahedral tensegrity-based rover prototype that requires a physics engine to simulate its motions

(Draft) Asymptotically Optimal Sampling-based Kinodynamic Planning

Abstract—Sampling-based planning algorithms are efficient practical solutions to motion planning challenges. Existing al-gorithms such as PRM ∗ and RRT ∗ take advantages of random geometric graph theory to answer motion planning queries. This theory requires solving the two-point boundary value problem (BVP) in the state space, which is generally considered to be difficult and impractical. This work presents a different theory of asymptotical optimality. It fills in the gap between optimal kinodynamic planning problems and sampling-based algorithms. The resulting contributions explain some open problems, e.g., the existence of BVP-free asymptotically optimal sampling-based kinodynamic algorithms, properties of a previously pro-posed heuristical algorithm RRT-BestNear. This work further presents new algorithms STABLE SPARSE-RRT(SST) and SST∗. Analysis and experimental results show that SST and SST ∗ are efficient, general, BVP-free, sampling-based optimal kinodynamic planning algorithms that are practical for a great variety of physical systems. I