A superlinear convergence feasible sequential quadratic programming algorithm for bipedal dynamic walking robot via discrete mechanics and optimal control

Abstract

Summary 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.

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

“…From Figures and , the peak commanded torque is less than 30 Nm, one‐fifth of the actuators' 150 Nm maximum . Furthermore, it is less than the literature . Therefore, the optimal robust controller of this paper is better than the others in previous studies .…”

“…Furthermore, it is less than the literature . Therefore, the optimal robust controller of this paper is better than the others in previous studies . Due to the cost function evaluation requires solving one optimization problem, therefore, the projected Fletcher‐Reeves conjugate gradient approach can be recommended for high‐dimensional bipedal dynamical systems.…”

“…During the numerical experiments, the parameters are selected from literature . Considering the performance metric of minimum moment and the specific cost of transport in Sun et al, we have the following results found in Figures to , as in state trajectory plots corresponding to a simulated gait of RABBIT. Ten steps are taken at an average walking rate of 0.78 m/s each step.…”

A Dai–Yuan conjugate gradient algorithm of linear equation constrained optimization approach for optimal robust controller of bipedal robots

“…In this subsection, the performance of Dai-Yuan approach proposed in this article is to be compared with classical Hestenes-Stiefel method and Fletcher-Reeves method for all the testing problems in CUTE library. 21,23 The methods are implemented by Matlab 7.1 code in double precision arithmetic. The numerical examples are performed on a PC computer with CPU Pentium 4, 2.40 GHz, and Windows XP operation system.…”

“…Three-link bipedal robot. [20][21][22] for control input versus time. Let u 1 ¼ t 1 ; u 2 ¼ t 2 ; as shown in Figure 3, and using the Dai-Yuan projection conjugate gradient optimization algorithm to solve the optimal robust controller makes the control input increase with the number of walking steps of the robot, and the robot can achieve dynamic walking with minimum energy.…”