Abstract
This paper presents a new nondeterministic motion planning algorithm for nonholonomic systems. Such systems are represented by a driftless control system with outputs. The presented approach combines two different methods: the endogenous configuration space approach and the Particle Filters. The former, fully deterministic, was originally dedicated to the motion planning problem for mobile manipulators. The latter, of stochastic approach, was designed for solving optimal estimation problems in non-linear non-Gaussian systems. A mixture of these methods results in a nondeterministic endogenous configuration space approach that outperforms the traditional one in regions where the classical inverse Jacobian algorithm loses convergence. In accordance with the Particle Filters approach the new algorithm consists of three major steps: prediction, update, and resampling. In contrast to its original version, the presented algorithm contains an additional step of dividing the particles into different subsets. Each subset is processed in a different way during the prediction phase. The performance of the new algorithm is illustrated by solving the motion planning problem for a rolling ball.
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References
Arulampalam, M.S., Maskell, S., Gordon, N.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Sig. Process. 50, 174–188 (2002)
Bolic, M., Djuric, P.M., Hong, S.: Resampling algorithms and architectures for distributed particle filters. IEEE Trans. Sig. Process. 53, 2442–2450 (2004)
Douc, R.: Comparison of resampling schemes for particle filtering. In: 4th International Symposium on Image and Signal Processing and Analysis (ISPA), pp. 64–69 (2005)
Doucet, A., Johansen, A.M.: A Tutorial on Particle Filtering and Smoothing: Fifteen years Later. In: Crisan, D., Rozovsky, B. (eds.) Handbook of Nonlinear Filtering. Oxford University Press (2009)
Gordon, N., Salmond, D., Smith, A.: Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In: IEE-Proceedings-F, vol. 140, pp. 107–113 (1993)
Janiak, M., Tchoń, K.: Constrained robot motion panning: Imbalanced jacobian algorithm vs. optimal control approach. In: Proc. 15th Int. MMAR Conf., Miedzyzdroje, pp. 25–30 (2010)
Janiak, M., Tchoń, K.: Towards constrained motion planning of mobile manipulators. In: IEEE Int. Conf. Robot. Automat., Anchorage, Alaska, pp. 4990–4995 (2010)
Pantrigo, J.J., Sanchez, A.: Hybridizing particle filters and population-based metaheuristics for dynamic optimization problems. In: Proc. of the V International Conf. on Hybrid Intelligent Systems, pp. 41–48. IEEE Computer Society Press, Washington, DC, USA (2005)
Ratajczak, A., Janiak, M.: Motion planning of an underactuated manipulators with state space constraints. Scientific Papers of Warsaw University of Technology 175(2), 495–504 (2010) (in Polish)
Ratajczak, A., Karpiska, J., Tchoń, K.: Task-priority motion planning of underactuated systems: an endogenous configuration space approach. Robotica 28, 885–892 (2009)
Tchoń, K., Jakubiak, J.: Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms. Int. J. Contr. 76(14), 1387–1419 (2003)
Tchoń, K., Jakubiak, J.: Extended Jacobian inverse kinematics algorithm for non-holonomic mobile robots. Int. J. Contr. 79, 895–909 (2006)
Zhou, E., Fu, M.C., Marcus, S.I.: A particle filtering framework for randomized optimization algorithms. In: Proc. of the 40th Conf. on Winter Simulation, WSC 2008, pp. 647–654 (2008)
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Janiak, M. (2012). Motion Planning of Nonholonomic Systems – Nondeterministic Endogenous Configuration Space Approach. In: Kozłowski, K. (eds) Robot Motion and Control 2011. Lecture Notes in Control and Information Sciences, vol 422. Springer, London. https://doi.org/10.1007/978-1-4471-2343-9_26
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DOI: https://doi.org/10.1007/978-1-4471-2343-9_26
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