The Provable Virtue of Laziness in Motion Planning

The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms that only evaluate edges along shortest paths between the source and target. These algorithms were designed to minimize the number of edge evaluations in settings where edge evaluation dominates the running time of the algorithm; but how close to optimal are LazySP algorithms in terms of this objective? Our main result is an analytical upper bound, in a probabilistic model, on the number of edge evaluations required by LazySP algorithms; a matching lower bound shows that these algorithms are asymptotically optimal in the worst case

Bayesian Active Edge Evaluation on Expensive Graphs

Robots operate in environments with varying implicit structure. For instance, a helicopter flying over terrain encounters a very different arrangement of obstacles than a robotic arm manipulating objects on a cluttered table top. State-of-the-art motion planning systems do not exploit this structure, thereby expending valuable planning effort searching for implausible solutions. We are interested in planning algorithms that actively infer the underlying structure of the valid configuration space during planning in order to find solutions with minimal effort. Consider the problem of evaluating edges on a graph to quickly discover collision-free paths. Evaluating edges is expensive, both for robots with complex geometries like robot arms, and for robots with limited onboard computation like UAVs. Until now, this challenge has been addressed via laziness i.e. deferring edge evaluation until absolutely necessary, with the hope that edges turn out to be valid. However, all edges are not alike in value - some have a lot of potentially good paths flowing through them, and some others encode the likelihood of neighbouring edges being valid. This leads to our key insight - instead of passive laziness, we can actively choose edges that reduce the uncertainty about the validity of paths. We show that this is equivalent to the Bayesian active learning paradigm of decision region determination (DRD). However, the DRD problem is not only combinatorially hard, but also requires explicit enumeration of all possible worlds. We propose a novel framework that combines two DRD algorithms, DIRECT and BISECT, to overcome both issues. We show that our approach outperforms several state-of-the-art algorithms on a spectrum of planning problems for mobile robots, manipulators and autonomous helicopters

Multi-Agent Persistent Task Performance

A method to control a system of robots to persistently perform a task while operating under a constraint such as battery life is presented. Persistently performing a task is defined as continuously executing the task without a break or stopping due to low battery constraints or lack of capabilities of a particular agent. If an agent is no longer able to execute the task it must be replaced by one that can continue the execution of the task. This is achieved through the utilization of two distinctions of agent roles: workers and helpers. This method is focused on addressing problems that require task handoffs where a second robot physically replaces a robot that has run low on battery. The worker agents are assigned the tasks, and perform the tasks until the constraint prevents further performance. Once a worker agent has reached a low battery threshold a task handoff is performed with a helper agent. This method utilizes a proactive approach in performing these handoffs by predicting the time and place that a worker will reach a low battery threshold and need to perform a handoff. This decreases the time necessary to respond to a low battery in these problems compared to prior developed reactive methods. As a result the total time needed by the multi agent team to complete a set of tasks is decreased. In this paper, the method is demonstrated utilizing a physics based simulator to model the behavior of the multi agent team. Experiments are run over three standard problems requiring agent task handoffs: sentry, inspection, and coverage. These demonstrate the effectiveness of the method when compared against the existing reactive methods

Asymptotically near-optimal RRT for fast, high-quality, motion planning

We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary graph, which we call the lower-bound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRG and RRT*) with little running-time overhead when compared to RRT

Adaptively Informed Trees (AIT*): Fast Asymptotically Optimal Path Planning through Adaptive Heuristics

Informed sampling-based planning algorithms exploit problem knowledge for better search performance. This knowledge is often expressed as heuristic estimates of solution cost and used to order the search. The practical improvement of this informed search depends on the accuracy of the heuristic. Selecting an appropriate heuristic is difficult. Heuristics applicable to an entire problem domain are often simple to define and inexpensive to evaluate but may not be beneficial for a specific problem instance. Heuristics specific to a problem instance are often difficult to define or expensive to evaluate but can make the search itself trivial. This paper presents Adaptively Informed Trees (AIT*), an almost-surely asymptotically optimal sampling-based planner based on BIT*. AIT* adapts its search to each problem instance by using an asymmetric bidirectional search to simultaneously estimate and exploit a problem-specific heuristic. This allows it to quickly find initial solutions and converge towards the optimum. AIT* solves the tested problems as fast as RRT-Connect while also converging towards the optimum.Comment: IEEE International Conference on Robotics and Automation (ICRA) 2020, 6 + 2 pages, 5 figures, video available at https://youtu.be/twM723QM9T