Online Adaptive Motion Generation for Humanoid Locomotion on Non-Flat Terrain Via Template Behavior Extension

For humanoid robots, online motion generation on non-flat terrain remains an ongoing research challenge. Computational complexity is one of the primary restrictions that preclude motion planners from generating adaptive behaviors online. In this paper, we investigate this problem and decom- pose it into two sequential components: an Efficient Behavior Generator (EBG) and a Nonlinear Centroidal Model Predictive Controller (NC-MPC). The EBG is responsible for optimizing the physically feasible whole-body template behaviors, which can provide reliable warm-starts for NC-MPC, thereby greatly reducing the computational effort of online planning. With tailored objective function and feet complementary constraints, the EBG can search for a near-optimal solution after several iterations within seconds for different behaviors including walk- ing, running, and jumping, even with intuitive initial guesses. To make the template behaviors extensible when the robot encounters possible different scenarios, the NC-MPC is proposed to regenerate the reactive motion online to adapt it to the real local environment. Finally, we validate the effectiveness of synthesizing EBG and NC-MPC for humanoid locomotion on non-flat terrain in simulation and on the real humanoid robot BHR7P. Note to Practitioners— For current humanoid robots, dynam- ically traversing non-flat terrain such as stairs, slopes, and gaps in the real world presents a significant challenge. In this paper, we propose an adaptive motion planner for humanoid robots to traverse non-flat terrain, which is properly integrated into the closed loop of online control. Considering computational complexity and motion extensibility, the planner consists of two parts: an efficient behavior generator performed offline and a nonlinear model predictive controller performed online. The behavior generator can efficiently generate template behaviors for the humanoid robot, including various gaits such as walk- ing, running, and jumping. To make these template behaviors adaptable, a nonlinear model predictive controller based on Manuscript received 12 September 2023; accepted 17 October 2023. This article was recommended for publication by Associate Editor J. Gu and Editor P. Rocco upon evaluation of the reviewers’ comments. This work was supported in part by the National Natural Science Foundation of China under Grant 62073041 and Grant 61973039 and in part by the 111 Project under Grant B08043. (Corresponding author: Zhangguo Yu.) Xiang Meng and Zelin Huang are with the School of Mechatronical Engineering, Beijing Institute of Technology (BIT), Beijing 100081, China. Zhangguo Yu, Xuechao Chen, Fei Meng, and Qiang Huang are with the School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China, also with the Key Laboratory of Biomimetic Robots and Systems, Ministry of Education, Beijing 100081, China, and also with the National Key Lab of Autonomous Intelligent Unmanned Systems, Beijing 100081, China (e-mail: yuzg@bit.edu.cn). This article has supplementary material provided by the authors and color versions of one or more figures available at https://doi.org/10.1109/ TASE.2023.3327819. Digital Object Identifier 10.1109/TASE.2023.3327819 the centroidal dynamics model is developed to plan reactive motions online. It can extend template behaviors to fit potentially different scenarios in practice. The proposed method is validated in simulations and experiments with the humanoid robot BHR7P. Furthermore, this method can be applied to legged robots or systems that need to move dynamically on non-flat terrain, such as quadruped and hexapod robots.