Abstract
This chapter presents the analysis and design of Dynamic Surface Control (DSC) with the application to biped walking with a variable step size. Under the assumption that the biped model consists of a single-leg support, a double impact, and a double-leg support phase model, the DSC is applied to the model which is a piecewise multi-input multi-output nonlinear system. Once the system becomes closed-loop with DSC, piecewise augmented error dynamics with provable stability properties are derived in the form of a piecewise linear system subject to exogenous inputs. Based on the error dynamics, a convex optimization problem is formulated to estimate the ellipsoidal error bound to guarantee the piecewise quadratic boundedness. Finally, the performance of DSC for the biped walking with a variable step size will be estimated by calculating a piecewise ellipsoidal error bound numerically and validated via simulation.
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References
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)
Canudas-De-Wit, C., Olsson, H., Astrom, K.J., Lischinsky, P.: A new model for control of system with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995)
Chemori, A., Loria, A.: Control of a planar underactuated biped on a complete walking cycle. IEEE Trans. Autom. Control 49(5), 838–843 (2004)
Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E.R., Canudas-De-Wit, C., Grizzle, J.W.: Rabbit: a testbed for advanced control theory. IEEE Control Syst. Mag. 23, 57–79 (2003)
Choi, J.-W., Song, B., Park, T.W.: A study on modeling of gait cycle and its zmp variation for biped. In: Proceedings of KSMTE Autumn Conference, Suwon, Korea, pp. 57–62 (2005)
Grant, M., Boyd, S.: CVX: Matlab software for disciplined convex programming, version 1.21. http://cvxr.com/cvx/ (2011)
Greenwood, D.T.: Principles of Dynamics, 2nd edn. Prentice Hall, New York (1988)
Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: analysis via systems with impulse effects. IEEE Trans. Autom. Control 46(1), 51–64 (2001)
Marhefka, D.W., Orin, D.: Simulation of contact using a nonlinear damping model. In: Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis, MN, pp. 1662–1668 (1996)
Mu, X., Wu, Q.: Development of a complete dynamic model of a planar five-link biped and sliding mode control of its locomotion during the double support phase. Int. J. Control 77(8), 789–799 (2004)
Park, J.H., Kim, K.D.: Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control. In: Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium, pp. 3528–3533 (1998)
Plestan, F., Grizzle, J.W., Westervelt, E.R., Abba, G.: Stable walking of a 7-dof biped robot. IEEE Trans. Robot. Autom. 19(4), 653–668 (2003)
Spong, M.W., Vidyasagar, M.: Robot Dynamics and Control. Wiley, New York (1991)
Sturm, J.F.: Using SeDuMi 1.02, a matlab toolbox for optimization over symmetric cones
Tzafestas, S., Raibert, M., Tzafestas, C.: Robust sliding-mode control applied to a 5-link biped robot. J. Intell. Robot. Syst. 15, 67–133 (1996)
Vukobratovic, M., Borovac, B., Surla, D., Stokic, D.: Biped Locomotion. Springer, Berlin (1990)
You, B.-J., Oh, Y.-H., Choi, Y.-J.: Survey on humanoid researches. J. Korean Soc. Precis. Eng. 21(7), 15–21 (2004)
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Song, B., Hedrick, J.K. (2011). Biped Robot Control. In: Dynamic Surface Control of Uncertain Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-632-0_9
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DOI: https://doi.org/10.1007/978-0-85729-632-0_9
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