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1. Learning Proofs of Motion Planning Infeasibility

   https://doi.org/10.15607/RSS.2021.XVII.064  

   Li, Sihui; Dantam, Neil T (July 2021, Robotics: Science and Systems)

   Shell, Dylan A; Toussaint, Marc (Ed.)

   We present a learning-based approach to prove infeasibility of kinematic motion planning problems. Sampling-based motion planners are effective in high-dimensional spaces but are only probabilistically complete. Consequently, these planners cannot provide a definite answer if no plan exists, which is important for high-level scenarios, such as task-motion planning. We propose a combination of bidirectional sampling-based planning (such as RRT-connect) and machine learning to construct an infeasibility proof alongside the two search trees. An infeasibility proof is a closed manifold in the obstacle region of the configuration space that separates the start and goal into disconnected components of the free configuration space. We train the manifold using common machine learning techniques and then triangulate the manifold into a polytope to prove containment in the obstacle region. Under assumptions about learning hyper-parameters and robustness of configuration space optimization, the output is either an infeasibility proof or a motion plan. We demonstrate proof construction for 3-DOF and 4-DOF manipulators and show improvement over a previous algorithm. 

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2. Exponential Convergence of Infeasibility Proofs for Kinematic Motion Planning

   Li, Sihui; Dantam, Neil (January 2023, Algorithmic Foundations of Robotics XV)

   Proving motion planning infeasibility is an important part of a complete motion planner. Common approaches for high-dimensional motion planning are only probabilistically complete. Previously, we presented an algorithm to construct infeasibility proofs by applying machine learning to sampled configurations from a bidirectional sampling-based planner. In this work, we prove that the learned manifold converges to an infeasibility proof exponentially. Combining prior approaches for sampling-based planning and our converging infeasibility proofs, we propose the term asymptotic completeness to describe the property of returning a plan or infeasibility proof in the limit. We compare the empirical convergence of different sampling strategies to validate our analysis. 

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3. Asymptotically Optimal Kinodynamic Planning Using Bundles of Edges

   https://doi.org/10.1109/ICRA48506.2021.9560836  

   Shome, Rahul; Kavraki, Lydia E. (May 2021, 2021 IEEE International Conference on Robotics and Automation (ICRA))

   null (Ed.)

   Using sampling to estimate the connectivity of high-dimensional configuration spaces has been the theoretical underpinning for effective sampling-based motion planners. Typical strategies either build a roadmap, or a tree as the underlying search structure that connects sampled configurations, with a focus on guaranteeing completeness and optimality as the number of samples tends to infinity. Roadmap-based planners allow preprocessing the space, and can solve multiple kinematic motion planning problems, but need a steering function to connect pairwise-states. Such steering functions are difficult to define for kinodynamic systems, and limit the applicability of roadmaps to motion planning problems with dynamical systems. Recent advances in the analysis of single query tree-based planners has shown that forward search trees based on random propagations are asymptotically optimal. The current work leverages these recent results and proposes a multi-query framework for kinodynamic planning. Bundles of kinodynamic edges can be sampled to cover the state space before the query arrives. Then, given a motion planning query, the connectivity of the state space reachable from the start can be recovered from a forward search tree reasoning about a local neighborhood of the edge bundle from each tree node. The work demonstrates theoretically that considering any constant radial neighborhood during this process is sufficient to guarantee asymptotic optimality. Experimental validation in five and twelve dimensional simulated systems also highlights the ability of the proposed edge bundles to express high-quality kinodynamic solutions. Our approach consistently finds higher quality solutions compared to SST, and RRT, often with faster initial solution times. The strategy of sampling kinodynamic edges is demonstrated to be a promising new paradigm. 

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4. Motion Planning around Obstacles with Convex Optimization

   Tobia Marcucci, Mark Petersen2 (May 2022, ArXivorg)

   Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time. 

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5. Sample-Driven Connectivity Learning for Motion Planning in Narrow Passages

   Li, Sihui; Dantam, Neil T (May 2023, International Conference on Robotics and Automation)

   Sampling-based motion planning works well in many cases but is less effective if the configuration space has narrow passages. In this paper, we propose a learning-based strategy to sample in these narrow passages, which improves overall planning time. Our algorithm first learns from the configuration space planning graphs and then uses the learned information to effectively generate narrow passage samples. We perform experiments in various 6D and 7D scenes. The algorithm offers one order of magnitude speed-up compared to baseline planners in some of these scenes. 

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