Time Optimal Planning-Based High-Speed Running Motion Generation for Humanoid Robots with Safety Constraints

Humanoid bipedal robot is a typical form of human-like robot with highly underactuated and nonlinear characteristics, which can bring many challenges to robot planning and control. How to demonstrate the strong locomotion ability through control strategies has always been an interesting issue that researchers have explored in depth. Under the limited actuator abilities, the realization of high-speed running for humanoid robots is also an important reflection of high locomotion ability, flexibility and strong stability. In this paper, a time optimal planning-based motion generation method is proposed to realize the high-speed running task of humanoid robots. First, since the humanoid robots usually have many degrees of freedom throughout the whole body, to reduce the computational complexity, a simplified 7-link dynamic model is established. Further, considering the time cost, running speed and security concerns, a multi-constraint time optimal problem within a single gait cycle is constructed, which can reduce the solution space dimension and be extended to generate trajectories of multiple cycles. Since the optimal control problem with constraints is difficult to solve, on the basis of the Legendre-Gauss-Radau (LGR) pseudospectral method, the states and the input trajectories of the system are discretized through a small number of collocation points, which can be transformed into a nonlinear programming problem to quickly find the optimal solution. By applying the proposed scheme, continuous states and input trajectories can be directly generated, and the target running speed is realized in the shortest time, which ensures that multiple constraints are limited within given ranges, simultaneously. Finally, numerical simulations are carried out to validate the effectiveness of the presented motion generation method.