Abstract
An optimal control problem to find the fastest collision-free trajectory of a robot is presented. The dynamics of the robot is governed by ordinary differential equations. The collision avoidance criterion is a consequence of Farkas’s lemma and is included in the model as state constraints. Finally an active set strategy based on backface culling is added to the sequential quadratic programming which solves the optimal control problem.
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Berkovitz, L.D.: Convexity and Optimization in ℝn. John Wiley & Sons, New York (2001)
Cohen, J.D., Lin, M.C., Manocha, D., Ponamgi, M.K.: I-collide: An Interactive and Exact Collision Detection System for Large-Scaled Environments. In: Symposium on Interactive 3D Graphics, pp. 189–196. ACM Siggraph (1995)
Diehl, M., Bock, H.G., Diedam, H., Wieber, P.B.: Fast Direct Multiple Shooting Algorithms for Optimal Robot Control. In: Fast Motions in Biomechanics and Robotics, pp. 65–94. Springer (2005)
Gerdts, M.: Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems. Journal of Optimization Theory and Applications 117, 267–294 (2003)
Gerdts, M.: Optimal Control of Ordinary Differential Equations and Differential-Algebraic Equations. Fakultät für Mathematik und Physik, Universität Bayreuth, Bayreuth (2006)
Gerdts, M., Henrion, R., Hömberg, D., Landry, C.: Path Planning and Collision Avoidance for Robots. Numer. Algebra Control Optim. 3, 437–463 (2012)
Gilbert, E.G., Hong, S.M.: A New Algorithm for Detecting the Collision of Moving Objects. In: IEEE Proc. Int. Conf. on Robotics and Automation, vol. 1, pp. 8–14 (1989)
Gilbert, E.G., Johnson, D.W.: Distance Functions and their Application to Robot Path Planning in the Presence of Obstacles. IEEE Journal of Robotics and Automation 1, 21–30 (1985)
Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization. SIAM Rev. 47, 99–131 (2005)
LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006)
Mirtich, B.: V-Clip: Fast and Robust Polyhedral Collision Detection. Mitsubishi Electronics Research Laboratory (1997)
Murray, R.M., Sastry, S.S., Li, Z.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Inc., Boca Raton (1994)
Schittkowski, K.: On the Convergence of a Sequential Quadratic Programming Method with an Augmented Lagrangean Line Search Function. In: Mathematische Operationsforschung und Statistik. Series Optimization, vol. 14, pp. 197–216 (1983)
Vaněček Jr., G.: Back-Face Culling Applied to Collision Detection of Polyhedra. Journal of Visualization and Computer Animation 5, 55–63 (1994)
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Landry, C., Gerdts, M., Henrion, R., Hömberg, D. (2013). Path-Planning with Collision Avoidance in Automotive Industry. In: Hömberg, D., Tröltzsch, F. (eds) System Modeling and Optimization. CSMO 2011. IFIP Advances in Information and Communication Technology, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36062-6_11
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DOI: https://doi.org/10.1007/978-3-642-36062-6_11
Publisher Name: Springer, Berlin, Heidelberg
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