Abstract
We develop trajectory planners for a class of second-order underactuated mechanical systems called kinematically controllable systems. For kinematically controllable systems, the problem of planning fast collision-free trajectories can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. This paper describes efficient path planners using randomized algorithms and dynamic programming to solve the path planning problem for the kinematic system. The resulting kinematic paths are time scaled to produce fast trajectories.
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
http://msl.cs.uiuc.edu/msl//msl/, “Motion Strategy Library,” Dept. of Computer Science, Univ. of Illinois, Urbana-Champaign.
J. Barraquand and J. C–Latombe, “Nonholonomic multibody mobile robots: Controllability and motion planning in presence of obstacles,” Algorithmica, vol. 10, no. 2–3–4, pp. 121 – 155, 1993.
J. E. Bobrow, S. Dubowsky and J. S. Gibson, “Time-optimal control of robotic manipulators along specified paths,” International Journal of Robotics Research, vol. 4, no. 3, pp. 3–17, 1985.
R. Bohlin, “Path planning in practice; lazy evaluation on a multiresolution grid,” in Proc. IEEE Conference on Intelligent Robots and Systems, October 2001.
F. Bullo and K. M. Lynch, “Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems,” IEEE Transactions on Robotics and Automation, vol. 17, no. 4, pp. 402–412, 2001.
B. Donald, P. Xavier, J. Canny and J. Reif, “Kinodynamic motion planning,” Journal of Association for Computing Machinery (ACM), vol. 40, no. 5, pp. 1048–1066, 1993.
N. Faiz, S. Agrawal, and R. M. Murray, “Differentially flat systems with inequality constraints: An approach to real-time feasible trajectory generation,” AIAA Journal of Guidance, Control and Dynamics, vol. 24, no. 2, pp. 219–227, 2001.
M. Fliess, J. Levine, P. Martin and P. Rouchon, “Flatness and defect of nonlinear systems: Introduction, theory and examples,” International Journal of Control, vol. 61, no. 6, pp. 1327–1361, 1995.
D. Hsu, R. Kindel, J.-C. Latombe and S. Rock, “Randomized motion planning with moving obstacles,” International Journal of Robotics Research, vol. 21, no. 3, pp. 233–255, 2002.
T. Karatas and F. Bullo, “Randomized searches and nonlinear programming in trajectory planning,” in Proc. IEEE Conference on Decision and Control, pp. 5032–5037, 2001.
L. E. Kavraki, P. Svestka, J.-C. Latombe, and M. Overmars, “Probabilistic Roadmaps for Path Planning in High Dimensional Configuration Spaces,” IEEE Transactions on Robotics and Automation, vol. 12, no. 4, pp. 566580, 1996.
J.-P. Laumond, P. Jacobs, M. Taix and R. M. Murray, “A motion planner for nonholonomic mobile robots,” IEEE Transactions of Robotics and Automation, vol. 10, no. 5, pp. 121–155, 1993.
S. M. LaValle and J. Kuffner, “Randomized kinodynamic planning,” International Journal of Robotics Research, vol. 20, no. 5, pp. 378–400, 2001.
K. M. Lynch and M. Mason, “Stable pushing: mechanics, controllability and planning,” International Journal of Robotics Research, vol. 15, no. 6, pp. 533–556, 1996.
K. M. Lynch, N. Shiroma, H. Arai and K. Tanie, “Collision free trajectory planning for a 3-dof robot with a passive joint,” International Journal of Robotics Research, vol. 19, no. 12, pp. 1171–1184, Dec. 2000.
P. Martin and P. Rouchon, “Any controllable (driftless) system with 3 inputs and 5 states is flat,” System and Control Letters, vol. 25, no. 3, pp. 167–173, 1995.
J. Reif and H. Wang, “Non-uniform discretization approximations for kinodynamic motion planning and its applications,” in Workshop on the Algorithmic Foundation of Robotics (WAFR, 96), (J. P. Laumond and M. Overmars eds.), pp. 97–112, 1996.
K. G. Shin and N. D. McKay, “Minimum time-control of robotic manipulators with geometric path constraints,” IEEE Transactions on Automatic Control, vol. 30. no. 6, pp. 531–541, 1985.
P. Xavier and B. Donald, “Provably good approximation algorithms for optimal kinodynamic planning: robots with decoupled dynamics bounds,” Algorithmica, vol. 14, no. 6, pp. 443–479, 1995.
P. Xavier and B. Donald, “Provably good approximation algorithms for optimal kinodynamic planning for cartesian robots and open chain manipulators,” Algorithmica, vol. 14, no. 6, pp. 480–530, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Choudhury, P., Lynch, K.M. (2004). Trajectory Planning for Kinematically Controllable Underactuated Mechanical Systems. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-45058-0_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07341-0
Online ISBN: 978-3-540-45058-0
eBook Packages: Springer Book Archive