A superlinear convergence feasible sequential quadratic programming algorithm for bipedal dynamic walking robot via discrete mechanics and optimal control
Zhongbo Sun
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Search for more papers by this authorCorresponding Author
Yantao Tian
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Correspondence to: Yantao Tian, College of Communication Engineering and Key Laboratory of Bionic Engineering of Ministry of Education, Jilin University, Changchun, 130025, China.
E-mail: [email protected]
Search for more papers by this authorHongyang Li
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Search for more papers by this authorJing Wang
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Search for more papers by this authorZhongbo Sun
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Search for more papers by this authorCorresponding Author
Yantao Tian
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Correspondence to: Yantao Tian, College of Communication Engineering and Key Laboratory of Bionic Engineering of Ministry of Education, Jilin University, Changchun, 130025, China.
E-mail: [email protected]
Search for more papers by this authorHongyang Li
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Search for more papers by this authorJing Wang
Key Laboratory of Bionic Engineering of Ministry of Education and College of Communication Engineering, Jilin University, Changchun, 130025 China
Search for more papers by this authorSummary
For periodic gait optimization problem of the bipedal walking robot, a class of global and feasible sequential quadratic programming algorithm (FSQPA) is proposed based on discrete mechanics and optimal control. The optimal controls and trajectories are solved by the modified FSQPA. The algorithm can rapidly converge to a stable gait cycle by selecting an appropriate initial gait; otherwise, the algorithm only needs one step correction that generates a stable gait cycle. Under appropriate conditions, we provide a rigorous proof of global convergence and well-defined properties for the FSQPA. Numerical results show that the algorithm is feasible and effective. Meanwhile, it reveals the movement mechanism in the process of bipedal dynamic walking, which is the velocity oscillations. Furthermore, we overcome the oscillatory behavior via the FSQPA, which makes the bipedal robot walk efficiently and stably on even terrain. The main result is illustrated on a hybrid model of a compass-like robot through simulations and is utilized to achieve bipedal locomotion via FSQPA. To demonstrate the effectiveness of the high-dimensional bipedal robot systems, we will conduct numerical simulations on the model of RABBIT with nonlinear, hybrid, and underactuated dynamics. Numerical simulation results show that the FSQPA is feasible and effective. Copyright © 2015 John Wiley & Sons, Ltd.
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