Abstract—One of the clear problems encountered in the dynamic response of the biped robot is the discontinuity of the actuating torques/ground reaction forces at the transition instances during transferring form single support phase to double support phase and vice versa. Therefore, this paper suggests the linear transition function used in the biomechanics field for estimating the ground reaction forces during the double support phase such that gradual increase/decrease of the ground reaction forces can occur. The closure loop of the biped robot at the transition instances during DSP can be broken using the mentioned strategy. Consequently, the continuous dynamic response can be achieved. Two cases are simulated using the optimal control theory. The inverse dynamics-based optimization is preferred as a direct suboptimal tool because it can show less computation and easinessthan other optimal control approaches. Due to easiness of the finite difference approach, it is used for discretization of the dynamic equations and the imposed constraints to convert the dynamic optimal control problem into parameter optimization. The simulated case 1 have been used repeatedly in the literature, whereas the case 2 adopts the linear transition function of the ground reaction forces keeping the same generalized coordinates of the biped configuration at the transition instances. The results show the superiority of the suggested method to guarantee continuous actuating torques/ground reaction forces at the transition instances.
Index Terms—Biped robot, finite difference, optimization, suboptimal control.
Hayder F. N. Al-Shuka is with Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany (e-mail: hayder.al-shuka@rwth-aachen.de).
B. J. Corves is with Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany (e-mail: corves@igm.rwth-aachen.de ).
B. Vanderborght is with Department of Mechanical Engineering, VrijieUniversiteitBrussel, Brussel, Belgium (e-mail: bram.vanderborght@vub.ac.be).
Wen-Hong Zhu is with the Canadian Space Agency, Canada (e-mail:Wen-Hong.Zhu@asc-csa.gc.ca).
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Cite:Hayder F. N. Al-Shuka, Burkhard J. Corves, Bram Vanderborght, and Wen-Hong Zhu, "Finite Difference-Based Suboptimal Trajectory Planning of Biped Robot with Continuous Dynamic Response," International Journal of Modeling and Optimization vol. 3, no. 4, pp. 337-343, 2013.
