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 decompose 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 walking, 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, dynamically 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 walking, running, and jumping. To make these template behaviors adaptable, a nonlinear model predictive controller based on 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.

Smooth state switching and accurate speed tracking are important for the stability and reactivity of bipedal robots when running. However, previous studies have rarely been able to synthesize these two capabilities online. In this paper, we present an online running-gait generator for bipedal robots that allows for smooth state switching and accurate speed tracking. Considering a fluctuating height nature and computational expediency, the robot is represented by a simplified variable-height inverted-pendulum (VHIP) model. In order to achieve smooth state switching at the beginning and end of running, a segmented zero moment point (ZMP) trajectory optimization is proposed to automatically provide a feasible and smooth center-of-mass (CoM) trajectory that enables the robot to stably start or stop running at the given speed. To accurately track online the desired speed during running, we propose an iterative algorithm to compute target footholds, which allows for the robot to follow the interactive desired speed after the next two steps. Lastly, a numerical experiment and the simulation of online variable speed running were performed with position-controlled bipedal robot BHR7P, and the results verified the effectiveness of the proposed methods.

When position-controlled biped robot is blind walking on a uneven terrain at a high speed, huge foot contact impacts will be generated. However, traditional admitance control can't absorb the impact and stabilize the robot due to its slow response and Incompleteness. In this paper, we propose a control strategy including respectively designed swing leg control and support leg control with a new approach of control transition. For Swing leg control, double spring damping model is presented to optimize the admitance controller with faster response and better robustness, and a active foot height controller is also proposed to reduce the impact further. On the other hand, the control transition is accomplished by using a bionic fuzzy control. As a result, the foot contact impact can be reduced and the robot can blind walk fast on uneven terrain. Finally, the validity of the proposed strategy is confirmed by the simulation.

Knee-stretched walking is considered to be a human-like and energy-efficient gait. The strategy of extending legs to obtain vertical center of mass trajectory is commonly used to avoid the problem of singularities in knee-stretched gait generation. However, knee-stretched gait generation utilizing this strategy with toe-off and heel-strike has kinematics conflicts at transition moments between single support and double support phases. In this article, a knee-stretched walking generation with toe-off and heel-strike for the position-controlled humanoid robot has been proposed. The position constraints of center of mass have been considered in the gait generation to avoid the kinematics conflicts based on model predictive control. The method has been verified in simulation and validated in experiment.

Unmanned spherical robots are autonomous mobile platforms with a fully enclosed spherical shell, providing high stability and strong adaptability to complex terrains. However, existing pendulum or flywheel spherical robots often suffer from limited maneuverability, whereas complex hybrid actuation schemes tend to compromise system stability. To address these issues, this study proposes an improved pendulum-driven spherical robot with a mechanically decoupled actuation design, integrating a pendulum system and a circular gear rack turning mechanism. This design enables smooth linear rolling as well as rapid in-place rotation, significantly enhancing maneuverability and motion flexibility on complex terrains. A dynamic model of the spherical robot is established to describe the decoupled actuation mechanism, and a fuzzy proportional–derivative (PD) control strategy is designed for rolling and steering control. Simulation and prototype experiments were conducted to evaluate trajectory tracking, steering response, and terrain adaptability. The results demonstrate that the proposed spherical robot achieves path following and in-place turning with robust mobility.