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Sampling-based optimal kinodynamic planning with motion primitives

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Abstract

This paper proposes a novel sampling-based motion planner, which integrates in Rapidly exploring Random Tree star (\(\hbox {RRT}^{\star }\)) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree of feasible trajectories in the \(\hbox {RRT}^{\star }\) algorithm by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity.

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Notes

  1. This approach can be easily extended in case stronger invariance properties hold.

  2. In this section, a \({\varDelta }\) superscript is used to denote all variables that are associated with the grid state space, so as to distinguish them from their continuous state space counterpart.

  3. A system is STLA from a state \(\mathbf {q}\in Q\) if \(\forall T>0\) the reachable set of states from q in time \(0<t \le T\), \(\mathcal {R}(\mathbf {q}, \le T)\) contains a d-dimensional subset of \(\mathcal {N}\), where \(\mathcal {N}\) denotes the set of neighborhood states in terms of Euclidean distance, (Choset 2005).

  4. It is assumed that \(\mathcal {K}_f \ge 1\).

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Acknowledgements

This work is supported by the European Commission under the project UnCoVerCPS with Grant Number 643921.

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Authors and Affiliations

  1. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza L. Da Vinci 32, 20133, Milan, Italy

    Basak Sakcak, Luca Bascetta, Gianni Ferretti & Maria Prandini

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  1. Basak Sakcak
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  2. Luca Bascetta
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  3. Gianni Ferretti
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Correspondence to Basak Sakcak.

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Sakcak, B., Bascetta, L., Ferretti, G. et al. Sampling-based optimal kinodynamic planning with motion primitives. Auton Robot 43, 1715–1732 (2019). https://doi.org/10.1007/s10514-019-09830-x

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