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Asymptotically Optimal Path Planning for Robotic Manipulators: Multi-Directional, Multi-Tree Approach

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Abstract

In this paper, we present a novel algorithm – RGBMT* (Rapidly-exploring Generalized Bur Multi-Tree star), intended for asymptotically optimal motion planning for robotic manipulators in static environments. The main idea is the generation of local/extra trees rooted in random configurations, beside two main trees rooted in initial and goal configurations. Each local tree is expanded towards all other trees via bur of free configuration space (\(\mathcal {C}\)-space). Each node is assigned a cost-to-come value, which is then used to optimally connect (if possible) all nodes from local trees to a single main tree according to Bellman’s principle of optimality. The algorithm is provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost-surely to the optimum. Main and local trees are aptly grown in order to prevent exploring \(\mathcal {C}\)-space in regions which are unlikely to yield solutions. A comprehensive simulation study is performed analyzing runtimes and convergence rate, where RGBMT* is compared to state-of-the-art algorithms. Obtained results indicate some promising features of the proposed method.

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Code Availability

The code is available online at https://github.com/roboticsETF/RPMPLv2.git.

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Funding

This work has been supported by Ministry of education and science of Canton Sarajevo, grant no. 11-05-14-27164-1/19.

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Authors and Affiliations

  1. University of Sarajevo, Faculty of Electrical Engineering, Zmaja od Bosne bb, 71000, Sarajevo, Bosnia and Herzegovina

    Nermin Covic, Dinko Osmankovic & Bakir Lacevic

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  1. Nermin Covic
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  2. Dinko Osmankovic
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  3. Bakir Lacevic
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Contributions

All authors contributed to this work equally. Material preparation was done by Nermin Covic and Bakir Lacevic, while code writing, data collection and analysis were performed by Nermin Covic and Dinko Osmankovic. The first draft of the manuscript was written by Nermin Covic, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Nermin Covic.

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Dinko Osmankovic and Bakir Lacevic contributed equally to this work.

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Covic, N., Osmankovic, D. & Lacevic, B. Asymptotically Optimal Path Planning for Robotic Manipulators: Multi-Directional, Multi-Tree Approach. J Intell Robot Syst 109, 14 (2023). https://doi.org/10.1007/s10846-023-01893-4

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