Configuration Space Decomposition for Scalable Proxy Collision Checking in Robot Planning and Control

Verghese, Mrinal; Das, Nikhil; Zhi, Yuheng; Yip, Michael C.

doi:10.1109/lra.2022.3147458

Cited by 9 publications

(2 citation statements)

References 14 publications

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“…Although this description can be exact for polygonal obstacles, in general, an approximate decomposition of the free space is necessary. For this step, multiple practical algorithms are available (30)(31)(32)(33), as well as methods tailored to the complex configuration spaces of kinematic trees (34)(35)(36)(37). A second approximation is the trajectory parameterization, which is necessary to solve our problems numerically.…”

Section: Algorithm Properties and Guaranteesmentioning

confidence: 99%

Motion planning around obstacles with convex optimization

Marcucci,

Petersen,

von Wrangel

et al. 2023

Sci. Robot.

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From quadrotors delivering packages in urban areas to robot arms moving in confined warehouses, motion planning around obstacles is a core challenge in modern robotics. Planners based on optimization can design trajectories in high-dimensional spaces while satisfying the robot dynamics. However, in the presence of obstacles, these optimization problems become nonconvex and very hard to solve, even just locally. Thus, when facing cluttered environments, roboticists typically fall back to sampling-based planners that do not scale equally well to high dimensions and struggle with continuous differential constraints. Here, we present a framework that enables convex optimization to efficiently and reliably plan trajectories around obstacles. Specifically, we focus on collision-free motion planning with costs and constraints on the shape, the duration, and the velocity of the trajectory. Using recent techniques for finding shortest paths in Graphs of Convex Sets (GCS), we design a practical convex relaxation of the planning problem. We show that this relaxation is typically very tight, to the point that a cheap postprocessing of its solution is almost always sufficient to identify a collision-free trajectory that is globally optimal (within the parameterized class of curves). Through numerical and hardware experiments, we demonstrate that our planner, which we name GCS, can find better trajectories in less time than widely used sampling-based algorithms and can reliably design trajectories in high-dimensional complex environments.

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Section: Algorithm Properties and Guaranteesmentioning

confidence: 99%

Motion planning around obstacles with convex optimization

Marcucci,

Petersen,

von Wrangel

et al. 2023

Sci. Robot.

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show abstract

“…Other notable works tackle SDF reconstruction in dynamic environments with composite fields [13] and in very large environments using submaps [27]. Lastly, other related directions tackle learning cost fields for motion planning [6,9,33] from SDFs [11,16], navigating in a neural radiance fields [1] and learning neural fields for articulated [18] or deformable objects [35] for manipulation.…”

Section: Related Workmentioning

confidence: 99%

iSDF: Real-Time Neural Signed Distance Fields for Robot Perception

Ortiz¹,

Clegg²,

Dong³

et al. 2022

Preprint

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Finding and Optimizing Certified, Collision-Free Regions in Configuration Space for Robot Manipulators

Amice

Dai²,

Werner

et al. 2022

Springer Proceedings in Advanced Robotics

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We present an efficient method for certifying noncollision for piecewise-polynomial motion plans in algebraic reparametrizations of configuration space. Such motion plans include those generated by popular randomized methods including RRTs and PRMs, as well as those generated by many methods in trajectory optimization. Based on Sums-of-Squares optimization, our method provides exact, rigorous certificates of non-collision; it can never falsely claim that a motion plan containing collisions is collision-free. We demonstrate that our formulation is practical for real world deployment, certifying the safety of a twelve degree of freedom motion plan in just over a second. Moreover, the method is capable of discriminating the safety or lack thereof of two motion plans which differ by only millimeters.

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Configuration Space Decomposition for Scalable Proxy Collision Checking in Robot Planning and Control

Cited by 9 publications

References 14 publications

Motion planning around obstacles with convex optimization

Motion planning around obstacles with convex optimization

iSDF: Real-Time Neural Signed Distance Fields for Robot Perception

Finding and Optimizing Certified, Collision-Free Regions in Configuration Space for Robot Manipulators

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