Abstract
In this paper we propose a calculation method for the optimal trajectory of a biped locomotion machine which is based on inverse kinematics and inverse dynamics. First, the trajectory of the waist is expressed by a Fourier series, where the bases are selected appropriately so that the periodic boundary conditions are strictly satisfied. A biped locomotion machine establishes optimal walking by using kicking forces to the ground at the moment of switching legs. In order to include the effecs of the kicking forces, additional terms that indicate the impulsive forces at the moment of switching legs are included in the formulation. Then the angles of each joint are determined by inverse kinematics, and using inverse dynamics, the input torques of each joint are expressed in terms of Fourier coefficients. By defining the performance index as a quadratic form of the input torques, the motion planning problem is formulated as an optimization problem of the trajectory of the waist, whose paramaters are Fourier coefficients of the trajactory of the waist. Using the successive quadratic programming (SQP) method, the optimal trajectory of a biped locomotion machine is obtained.
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References
Tsujita K, Tsuchiya K (1997) An experimental study of a biped locomotion machine using reaction wheels. Experimental robotics IV. The 4th International Sysmposium: Lecture Notes in Control and Information Sciences 223, Springer, pp. 558–565
Bryson Jr AE, Yu-Chi H (1975) Applied optimal control. Hemisphere
Wada Y, Kawato M (1993) A neural network model for arm trajectory formulation using forward and inverse dynamics models. Neural Networks 6:919–932
Fernandes C, Gurvit L, Li ZX (1992) Optimal nonholonomic motion planning for a falling cat. Nonholonomic Motion Plann KAP:379–421
Akiyama T, Sakawa Y (1995) A motion planning of space robot using nonlinear planning method (in Japanese). SICE 31: 193–197
McGeer T (1990) Passive dynamic walking. Int J Robotics Res 9(2):62–81
Ming-Shaung J, Mansour JM (1988) Simulation of the double limb support phase of human gait. ASME J Biomech Eng 110:223–229
Audu ML, Davy DT (1985) The influence of muscle model complexity in musculoskeletal motion modeling. ASME J Biomech Eng 107:147–157
Tsai C-S, Mansour JM (1986) Swing phase simulation and design of above knee prostheses. ASME J Biomech Eng 108:65–72
Taga G, Yamaguchi Y, Shimizu H (1991) Self-organized control of bipedal locomtion (in Japanese). HOLONICS 2:131–151
Hurmuzlu Y (1993) Dynamics of bipedal gait. Part I. Objective functions and the contact event of a planar five-link biped. ASME J Appl Mech 60:331–336
Hurmuzlu Y (1993) Dynamics of bipedal gait. Part II. Stability anlaysis of a planar five-link biped. ASME J Appl Mech 60:337–343
Hurmuzlu Y (1994) On the measurement of dynamic stability of human locomotion. ASME J Biomech Eng 116:30–36
Takeuchi H, Ohtsuka T (1997) Optimal walking problem for biped robot (in Japanese). Proceedings of the 15th Annual Conference of the Robotics Society of Japan, vol. 1, pp 95–96
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Tsujita, K., Tsuchiya, K. & Kawano, Y. A study on optimal motion of a biped locomotion machine. Artif Life Robotics 3, 55–60 (1999). https://doi.org/10.1007/BF02481247
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DOI: https://doi.org/10.1007/BF02481247