Abstract
In this paper, we define semi-holonomic controllability (SHC) and a general task and motion planning framework. We give a perturbation algorithm that can take a prehensile task and motion planning (PTAMP) domain and create a jointly-controllable-open (JC-open) variant with practically identical semantics. We then present a decomposition-based algorithm that computes the reachability set of a problem instance if a controllability criterion is met. Finally, by showing that JC-open domains satisfy the controllability criterion, we can conclude that PTAMP is decidable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Schwartz, J.T., Sharir, M.: On the piano movers problem. ii. general techniques for computing topological properties of real algebraic manifolds. Advances in applied Mathematics 4(3) (1983) 298–351
Canny, J.: The complexity of robot motion planning. MIT press (1988)
Wilfong, G.: Motion planning in the presence of movable obstacles. In: Proceedings of the fourth annual symposium on Computational geometry, ACM (1988) 279–288
Alami, R., Laumond, J.P., Siméon, T.: Two manipulation planning algorithms. In: Proceedings of the Workshop on Algorithmic Foundations of Robotics. WAFR, Natick, MA, USA, A. K. Peters, Ltd. (1995) 109–125
Dacre-Wright, B., Laumond, J.P., Alami, R.: Motion planning for a robot and a movable object amidst polygonal obstacles. In: Robotics and Automation, 1992. Proceedings., 1992 IEEE International Conference on, IEEE (1992) 2474–2480
Vendittelli, M., Laumond, J.P., Mishra, B.: Decidability of robot manipulation planning: Three disks in the plane. In: WAFR. (2014)
Munkres, J.: Topology. Featured Titles for Topology Series. Prentice Hall, Incorporated (2000)
Canny, J.: Computing roadmaps of general semi-algebraic sets. The Computer Journal 36(5) (1993) 504–514
Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decompostion. In: Automata Theory and Formal Languages 2nd GI Conference Kaiserslautern, May 20–23, 1975, Springer (1975) 134–183
Hong, H.: An improvement of the projection operator in cylindrical algebraic decomposition. In: Proceedings of the international symposium on Symbolic and algebraic computation, ACM (1990) 261–264
Jurdjevic, V.: Geometric Control Theory. Cambridge Studies in Advanced Mathematics. Cambridge University Press (1997)
Sussman, H.: Lie brackets, real analyticity and geometric control. Differential Geometric Control Theory 27 (1982) 1–116
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Deshpande, A., Kaelbling, L.P., Lozano-Pérez, T. (2020). Decidability of Semi-Holonomic Prehensile Task and Motion Planning. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_35
Download citation
DOI: https://doi.org/10.1007/978-3-030-43089-4_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43088-7
Online ISBN: 978-3-030-43089-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)