[Paper Review] Parallelised Diffeomorphic Sampling-based Motion Planning

Tin Lai, Weiming Zhi+2 more|arXiv (Cornell University)|Aug 26, 2021

Robotic Path Planning Algorithms28 references4 citations

TL;DR

This paper proposes Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP), a framework that uses gradient-based diffeomorphisms to shape sampling distributions in sampling-based motion planners like RRT, enabling faster convergence to feasible solutions. By learning a continuous occupancy representation and applying GPU-accelerated parallel morphing of the sampling distribution, PDMP improves success rates and reduces time-to-solution without additional runtime cost, outperforming baseline methods in complex environments.

ABSTRACT

We propose Parallelised Diffeomorphic Sampling-based Motion Planning (PDMP). PDMP is a novel parallelised framework that uses bijective and differentiable mappings, or diffeomorphisms, to transform sampling distributions of sampling-based motion planners, in a manner akin to normalising flows. Unlike normalising flow models which use invertible neural network structures to represent these diffeomorphisms, we develop them from gradient information of desired costs, and encode desirable behaviour, such as obstacle avoidance. These transformed sampling distributions can then be used for sampling-based motion planning. A particular example is when we wish to imbue the sampling distribution with knowledge of the environment geometry, such that drawn samples are less prone to be in collisions. To this end, we propose to learn a continuous occupancy representation from environment occupancy data, such that gradients of the representation defines a valid diffeomorphism and is amenable to fast parallel evaluation. We use this to "morph" the sampling distribution to draw far fewer collision-prone samples. PDMP is able to leverage gradient information of costs, to inject specifications, in a manner similar to optimisation-based motion planning methods, but relies on drawing from a sampling distribution, retaining the tendency to find more global solutions, thereby bridging the gap between trajectory optimisation and sampling-based planning methods.

Motivation & Objective

• To bridge the gap between trajectory optimization and sampling-based motion planning by incorporating gradient information into sampling distributions.
• To develop a method that shapes sampling distributions using diffeomorphisms derived from cost gradients, such as environment occupancy or user-specified biases.
• To enable efficient, parallel sampling from informed distributions using GPU acceleration, without increasing runtime cost.
• To improve the success rate and time-to-solution of sampling-based planners like RRT and PRM in challenging, high-dimensional environments.
• To maintain probabilistic completeness while significantly reducing the number of collision-prone samples through morphed sampling distributions.

Proposed method

• The method constructs diffeomorphisms from gradients of a learned continuous occupancy representation, which encode obstacle avoidance and environmental geometry.
• These diffeomorphisms are used to transform a simple base sampling distribution into a more informative, morphed distribution that favors feasible configurations.
• The morphed sampling distribution is computed in parallel on the GPU, enabling fast, scalable generation of informed samples.
• The CPU handles the sequential tree-building process of sampling-based planners (e.g., RRT), while the GPU pre-fills a sample bucket with morphed samples.
• The framework integrates seamlessly with existing planners like RRT, RRT*, RRT-connect, and Lazy-PRM*, preserving their probabilistic completeness.
• A fallback mechanism uses uniform sampling when the GPU-generated bucket is empty, ensuring no performance degradation in worst-case scenarios.

Experimental results

Research questions

• RQ1 Can gradient information from environment occupancy or user-specified costs be used to shape sampling distributions in sampling-based motion planning?
• RQ2 Can diffeomorphisms derived from cost gradients be efficiently computed and applied in parallel to accelerate motion planning?
• RQ3 Does parallelized morphing of sampling distributions improve time-to-solution and success rate in complex motion planning environments?
• RQ4 Can the integration of GPU-accelerated sampling distribution shaping be achieved with no additional runtime cost in sequential planning pipelines?
• RQ5 To what extent does PDMP improve performance over baseline sampling-based planners like RRT and RRT* in high-dimensional or cluttered environments?

Key findings

• PDMP-RRT* achieved an 80% success rate within 7 seconds in the divider environment, compared to under 50% for vanilla RRT* with uniform sampling.
• By 20 seconds, PDMP variants achieved near-perfect success rates, significantly outperforming their uniform-sampling counterparts.
• The number of morphed samples exceeded uninformed samples after just 1 second of planning, indicating efficient GPU utilization.
• The proportion of uninformed samples dropped to negligible levels after 0.2 seconds, showing rapid filling of the GPU-generated sample bucket.
• PDMP improved time-to-solution across all tested planners, with the most significant gains observed at low planning times.
• Lazy-PRM* performed poorly due to its multi-query nature and inability to find solutions within the time budget, highlighting the advantage of single-query PDMP variants.