Parallelised Diffeomorphic Sampling-based Motion Planning

Tin Lai, Weiming Zhi, Tucker Hermans, Fabio Ramos
Proceedings of the 5th Conference on Robot Learning, PMLR 164:81-90, 2022.

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 collision. 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 parallelise evaluation. We use this to “morph” the sampling distribution to draw far less 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v164-lai22a, title = {Parallelised Diffeomorphic Sampling-based Motion Planning}, author = {Lai, Tin and Zhi, Weiming and Hermans, Tucker and Ramos, Fabio}, booktitle = {Proceedings of the 5th Conference on Robot Learning}, pages = {81--90}, year = {2022}, editor = {Faust, Aleksandra and Hsu, David and Neumann, Gerhard}, volume = {164}, series = {Proceedings of Machine Learning Research}, month = {08--11 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v164/lai22a/lai22a.pdf}, url = {https://proceedings.mlr.press/v164/lai22a.html}, 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 collision. 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 parallelise evaluation. We use this to “morph” the sampling distribution to draw far less 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.} }
Endnote
%0 Conference Paper %T Parallelised Diffeomorphic Sampling-based Motion Planning %A Tin Lai %A Weiming Zhi %A Tucker Hermans %A Fabio Ramos %B Proceedings of the 5th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2022 %E Aleksandra Faust %E David Hsu %E Gerhard Neumann %F pmlr-v164-lai22a %I PMLR %P 81--90 %U https://proceedings.mlr.press/v164/lai22a.html %V 164 %X 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 collision. 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 parallelise evaluation. We use this to “morph” the sampling distribution to draw far less 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.
APA
Lai, T., Zhi, W., Hermans, T. & Ramos, F.. (2022). Parallelised Diffeomorphic Sampling-based Motion Planning. Proceedings of the 5th Conference on Robot Learning, in Proceedings of Machine Learning Research 164:81-90 Available from https://proceedings.mlr.press/v164/lai22a.html.

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