Optimization-based approach to path planning for closed chain robot systems

Szynkiewicz, Wojciech; Błaszczyk, Jacek

doi:10.2478/v10006-011-0052-8

Abstract

An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a "quasi-dynamic" NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used, which implements a nonlinear primal-dual interior-point method, one of the leading techniques for large-scale nonlinear optimization.

References

Abbasi-Yadkori, Y., Modayil, J. and Szepesvari, C. (2010). Extending rapidly-exploring random trees for asymptotically optimal anytime motion planning, IEEE/RSJ International Conference on Intelligent Robots and Systems, Taipei, Taiwan, pp. 127-132.
Search in Google Scholar
Asfour, T., Gyarfas, F., Azad, P. and Dillmann, R. (2006). Imitation learning of dual-arm manipulation tasks in humanoid robots, IEEE/RAS International Conference on Humanoid Robots (Humanoids 2006), Genoa, Italy, pp. 40-47.
Search in Google Scholar
Bell, B. M. and Burke, J. V. (2008). Algorithmic differentiation of implicit functions and optimal values, in C. H. Bischof, H. M. Bücker, P. D. Hovland, U. Naumann and J. Utke (Eds.), Advances in Automatic Differentiation, Springer, Berlin/Heidelberg, pp. 67-77.10.1007/978-3-540-68942-3_7
Search in Google Scholar
Benson, H. Y., Shanno, D. F. and Vanderbei, R. J. (2001). Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions, Technical Report ORFE-00-06, Operations Research and Financial Engineering, Princeton University, Princeton, NJ.
Search in Google Scholar
Benson, H. Y., Shanno, D. F. and Vanderbei, R. J. (2002). A comparative study of large-scale nonlinear optimization algorithms, Technical Report ORFE-01-04, Operations Research and Financial Engineering, Princeton University, Princeton, NJ.
Search in Google Scholar
Błaszczyk, J., Karbowski, A. and Malinowski, K. (2007). Object library of algorithms for dynamic optimization problems: Benchmarking SQP and nonlinear interior point methods, International Journal of Applied Mathematics and Computer Science 17(4): 515-537, DOI: 10.2478/v10006-007- 0043-y.
Search in Google Scholar
Błaszczyk, J. P. (2007). Object Library of Algorithms for Dynamic Optimization: A Study on Effectiveness of Sequential Quadratic Programming and Nonlinear Interior Point Methods, Ph.D. thesis, Warsaw University of Technology, Warsaw, (in Polish).
Search in Google Scholar
Byrd, R. H., Gilbert, J. C. and Nocedal, J. (2000). A trust region method based on interior point techniques for nonlinear programming, Mathematical Programming 89(1): 149-185.10.1007/PL00011391
Search in Google Scholar
Byrd, R. H., Hribar, M. E. and Nocedal, J. (1999). An interior point algorithm for large scale nonlinear programming, SIAM Journal on Optimization 9(4): 877-900.10.1137/S1052623497325107
Search in Google Scholar
Canny, J. (1988). The Complexity of Robot Motion Planning, MIT Press, Cambridge, MA.
Search in Google Scholar
Cortés, J., Siméon, T. and Laumond, J.-P. (2002). A random loop generator for planning the motions of closed kinematic chains using PRM methods, IEEE International Conference on Robotics and Automation ICRA, Washington, DC, USA, pp. 2141-2146.
Search in Google Scholar
Daniel, J. (1971). Approximate Minimisation of Functionals, Prentice Hall, Englewood Cliffs, NJ.
Search in Google Scholar
de Boor, C. (1978). Practical Guide to Splines, Springer, New York, NY/Heidelberg.10.1007/978-1-4612-6333-3
Search in Google Scholar
Dolan, E. D. and Moré, J. J. (2002). Benchmarking optimization software with performance profiles, Mathematical Programming 91(2): 201-213.10.1007/s101070100263
Search in Google Scholar
Fiacco, A. V. and McCormick, G. P. (1968). Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, NY/London.
Search in Google Scholar
Fiser, A., Do, R. and Sali, A. (2000). Modeling of loops in protein structure, Protein Science 9(9): 1753-1773.10.1110/ps.9.9.1753214471411045621
Search in Google Scholar
Fletcher, R. and Leyffer, S. (2002). Nonlinear programming without a penalty function, Mathematical Programming 91(2): 239-269.10.1007/s101070100244
Search in Google Scholar
Haegele, M., Nilsson, K. and Pires, J. N. (2008). Springer Handbook of Robotics, Springer, Berlin/Heidelberg.
Search in Google Scholar
Han, L. and Amato, N. (2000). A kinematics-based probabilistic roadmap method for closed chain systems, Workshop on Algoritmic Foundations of Robotics, Dartmouth, Hanover, NH, USA, pp. 233-245.
Search in Google Scholar
Han, L., Rudolph, L., Blumenthal, J. and Valodzin, I. (2006). Stratified deformation space and path planning for a planar closed chain with revolute joints, in S. Akella, N. Amato, W. Huang and B. Mishra (Eds.), International Workshop on Algorithmic Foundations of Robotics WAFR, Springer Tracts in Advanced Robotics, Vol. 47, Springer, New York, NY, pp. 235-250.
Search in Google Scholar
Kallmann, M., Aubel, A., Abaci, T. and Thalmann, D. (2003). Planning collision-free reaching motions for interactive object manipulation and grasping, Eurographics 22(3): 313-322.10.1111/1467-8659.00678
Search in Google Scholar
Kanehiro, F., Lamiraux, F., Kanoun, O., Yoshida, E. and Laumond, J.-P. (2008). A local collision avoidance method for non-strictly convex polyhedra, Proceedings of Robotics: Science and Systems (RSS) IV, Zurich, Switzerland, pp. 151-158.
Search in Google Scholar
Kavraki, L. E., Svestka, P., Latombe, J.-C. and Overmars, M. H. (1996). Probabilistic roadmaps for path planning in high-dimensional configuration spaces, IEEE Transactions on Robotics and Automation 12(4): 566-580.10.1109/70.508439
Search in Google Scholar
Kuffner, J. J. and LaValle, S. M. (2000). RRT-connect: An efficient approach to single-query path planning, IEEE International Conference on Robotics and Automation, San Francisco, CA, USA, pp. 995-1001.
Search in Google Scholar
Latombe, J.-C. (1991). Robot Motion Planning, Kluwer, Boston, MA.10.1007/978-1-4615-4022-9
Search in Google Scholar
LaValle, S. (2006). Planning Algorithms, Cambridge University Press, Cambridge.10.1017/CBO9780511546877
Search in Google Scholar
Liu, G. and Trinkle, J. (2005). Complete path planning for planar closed chains among point obstacles, Proceedings of Robotics: Science and Systems (RSS) I, Cambridge, MA, USA, pp. 33-40.
Search in Google Scholar
Merlet, J. (2000). Parallel Robots, Kluwer, Dordrecht.10.1007/978-94-010-9587-7
Search in Google Scholar
Morales, J. L., Nocedal, J., Waltz, R. A., Liu, G. and Goux, J.-P. (2001). Assessing the potential of interiormethods for nonlinear optimization, Technical Report OTC 2001/4, Optimization Technology Center, Northwestern University, Evanston, IL.
Search in Google Scholar
Ratliff, N., Zucker, M., Bagnell, J. A. and Srinivasa, S. (2009). CHOMP: Gradient optimization techniques for efficient motion planning, IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, pp. 489-494.
Search in Google Scholar
Szynkiewicz, W. (2003). Motion planning for multi-robot systems with closed kinematic chains, 9th IEEE International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 779-786.
Search in Google Scholar
Szynkiewicz, W. and Gosiewski, A. (1995). Motion space analysis and trajectory planning for dual-arm system, 2nd International Symposium on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 503-510.
Search in Google Scholar
Tang, X., Thomas, S. and Amato, N. (2007). Planning with reachable distances: Fast enforcement of closure constraints, IEEE International Conference on Robotics and Automation ICRA, Rome, Italy, pp. 2694-2699.
Search in Google Scholar
Tits, A. L.,Wächter, A., Bakhtiari, S., Urban, T. J. and Lawrence, C. (2002). A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties, Technical Report TR 2002-29, Institute for Systems Research, University of Maryland, College Park, MD.
Search in Google Scholar
Trinkle, J. and Milgram, R. (2002). Complete path planning for closed kinematic chains with spherical joints, International Journal of Robotics Research 21(9): 773-789.10.1177/0278364902021009119
Search in Google Scholar
Ulbrich, M., Ulbrich, S. and Vicente, L. N. (2004). A globally convergent primal-dual interior-point filter method for nonlinear programming, Mathematical Programming 100(2): 379-410.10.1007/s10107-003-0477-4
Search in Google Scholar
Vanderbei, R. J. and Shanno, D. F. (1997). An interior-point algorithm for non-convex nonlinear programming, Technical Report SOR-97-21, Statistics and Operations Research, Princeton University, Princeton, NJ.
Search in Google Scholar
Wächter, A. (2002). An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering, Ph.D. dissertation, Carnegie Mellon University, Pittsburgh, PA.
Search in Google Scholar
Wächter, A. and Biegler, L. T. (2000). Failure of global convergence for a class of interior point methods for nonlinear programming, Mathematical Programming 88(3): 565-574.10.1007/PL00011386
Search in Google Scholar
Wächter, A. and Biegler, L. T. (2005). Line search filter methods for nonlinear programming: Motivation and global convergence, SIAM Journal on Optimization 16(1): 1-31.10.1137/S1052623403426556
Search in Google Scholar
Wächter, A. and Biegler, L. T. (2006). On the implementation of a primal-dual interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming 106(1): 25-57.10.1007/s10107-004-0559-y
Search in Google Scholar
Waltz, R. A. and Plantenga, T. (2006). KNITRO 5.0 User's Manual, Ziena Optimization, Inc., http://www.ziena.com/docs/knitroman.pdf. http://www.ziena.com/docs/knitroman.pdf
Search in Google Scholar
Yakey, J., LaValle, S. and Kavraki, L. (2001). Randomized path planning for linkages with closed kineamtic chains, IEEE Transactions on Robotics and Automation 17(6): 951-958.10.1109/70.976030
Search in Google Scholar
Yershova, A. and LaValle, S. (2009). Motion planning for highly constrained spaces, in K. R. Kozłowski (Ed.) Robot Motion and Control 2009, Springer, Berlin/Heidelberg, pp. 297-306.10.1007/978-1-84882-985-5_27
Search in Google Scholar
Zefran, M. and Kumar, V. (1997). A variational calculus framework for motion planning, IEEE International Conference on Robotics and Automation ICRA, Albuquerque, NM, USA, pp. 415-420.
Search in Google Scholar
Zhang, J. and Knoll, A. (1995). An enhanced optimization approach for generating smooth robot trajectories in the presence of obstacles, Proceedings of the European Chinese Automation Conference, London, UK, pp. 263-268.
Search in Google Scholar
Zieliński, C. and Winiarski, T. (2010). Motion generation in the MRROC++ robot programming framework, International Journal of Robotics Research 29(4): 386-413.10.1177/0278364909348761
Search in Google Scholar

Optimization-based approach to path planning for closed chain robot systems

Abstract

Paradigm

My account