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Asymptotically optimal kinematic design of robots using motion planning

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Abstract

In highly constrained settings, e.g., a tentacle-like medical robot maneuvering through narrow cavities in the body for minimally invasive surgery, it may be difficult or impossible for a robot with a generic kinematic design to reach all desirable targets while avoiding obstacles. We introduce a design optimization method to compute kinematic design parameters that enable a single robot to reach as many desirable goal regions as possible while avoiding obstacles in an environment. Our method appropriately integrates sampling-based motion planning in configuration space into stochastic optimization in design space so that, over time, our evaluation of a design’s ability to reach goals increases in accuracy and our selected designs approach global optimality. We prove the asymptotic optimality of our method and demonstrate performance in simulation for (1) a serial manipulator and (2) a concentric tube robot, a tentacle-like medical robot that can bend around anatomical obstacles to safely reach clinically-relevant goal regions.

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Notes

  1. In fact, for any objective that can be defined with respect to a set of points on the robot, we can define the mapping f as \(f(\mathbf {d}, \mathbf {q}, \mathbf {k}) \mapsto \mathrm {Shape}(\mathbf {d}, \mathbf {q},\mathbf {k})\) for any objective-specific \({\mathcal {K}}_\mathrm {reach}\subseteq {\mathcal {K}}_\mathrm {robot}\).

  2. We remark that a default initial value of 1 for \(T_\mathrm {init}\) is suggested in Ingber (1993, 1989), and Ingber et al. (2012) and refer the reader to prior work, e.g., (Ben-Ameur 2004), for computing an appropriate \(T_\mathrm {init}\).

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Acknowledgements

We thank Alan Kuntz for his insights and feedback on the analysis, Robert J. Webster III for valuable discussions, and Luis G. Torres for his insights into design optimization and software for evaluating designs.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Cenk Baykal

  2. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Chris Bowen & Ron Alterovitz

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  1. Cenk Baykal
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  2. Chris Bowen
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  3. Ron Alterovitz
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Correspondence to Cenk Baykal.

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This research was supported in part by the National Science Foundation under Award IIS-1149965 and by the National Institutes of Health under Awards R01EB017467, R21EB017952, and R01EB024864.

This is one of several papers published in Autonomous Robots comprising the “Special Issue on Robotics Science and Systems”.

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Baykal, C., Bowen, C. & Alterovitz, R. Asymptotically optimal kinematic design of robots using motion planning. Auton Robot 43, 345–357 (2019). https://doi.org/10.1007/s10514-018-9766-x

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