Bipedal robots by their nature show both hybrid and underactuated system features which are not stable and controllable at every point of joint space. They are only controllable on certain fixed equilibrium points and some trajectories that are periodically stable between these points. Therefore, it is crucial to determine the trajectory in the control of walking robots. However, trajectory optimization causes a heavy computational load. Conventional methods to reduce the computational load weaken the optimization accuracy. As a solution, a variable time interval trajectory optimization method is proposed. In this study, optimization accuracy can be increased without additional computational time. Moreover, a five-link planar biped walking robot is designed, produced, and the dynamic walking is controlled with the proposed method. Finally, cost of transport (CoT) values are calculated and compared with other methods in the literature to reveal the contribution of the study. According to comparisons, the proposed method increases the optimization accuracy and decreases the CoT value.

Design of balancing control and the stability analysis of a biped during disturbed standing are investigated. A PD-based switching state feedback control is used to stabilize the biped at the upright position while satisfying the constraints between the feet and the ground. The concept of Lyapunov exponents is used for the stability analysis, and a stability region is determined. Furthermore, the stability region is compared and agrees well with the one from the previous work that predicts the feasible movement during which balance of human standing can be maintained. This agreement shows the potential of the concept of Lyapunov exponents to be used as a measure of balancing of human standing. The work contributes to bipedal balancing control, which is important in the development of bipedal robots.