This paper presents a complete planner and controller scheme for bipedal robots, designed to enhance robustness against external disturbances. The high-level planner utilizes model predictive control (MPC) to optimize both the foothold location and step duration based on the divergent component of motion (DCM) to increase the robustness of generated gaits. For low-level control, we employ a momentum-based observer capable of estimating external forces acting on both stance and swing legs. The full-body dynamics, incorporating estimated disturbances, are integrated into a weighted whole-body control (WBC) to obtain more accurate ground reaction forces needed by the momentum-based observer. This approach eliminates the dependency on foot-mounted sensors for ground reaction force measurement, distinguishing our method from other disturbance estimation methods that rely on direct sensor measurements. Additionally, the controller incorporates trajectory compensation mechanisms to mitigate the effects of external disturbances. The effectiveness of the proposed framework is validated through comprehensive simulations and experimental evaluations conducted on BRUCE, a miniature bipedal robot developed by Westwood Robotics (Los Angeles, CA, USA). These tests include walking under swing leg disturbances, traversing uneven terrain, and simultaneously resisting upper-body pushes.

This paper presents a complete planner and controller scheme to achieve balance and walking for a biped robot, which does not need to distinguish the robot’s dynamic model parameters. The high-level planner utilizes model predictive control to optimize both the foothold location and step duration based on the Divergent Component of Motion (DCM) model to enhance the robustness of generated gaits. For low-level control, we use quadratic programming (QP) to optimize the contact force distribution under the contact constraints to achieve the virtual wrench exerted on the base of the robot. Then, the joint torques sent to the robot are derived from three parts: first, the torques mapped from the contact force; second, the swing leg tracking; and third, the stance foot stabilization. The simulation and experiment on BRUCE, a miniature bipedal robot from Westwood Robotics (Los Angeles, CA, USA), testify to the performance of the control scheme, including push recovery, Center of Mass (CoM) tracking, and omnidirectional walking.

This article introduces a novel perspective on designing a stepping controller for bipedal robots. Typically, designing a state-feedback controller to stabilize a bipedal robot to a periodic orbit of step-to-step (S2S) dynamics based on a reduced-order model (ROM) can achieve stable walking. However, the model discrepancies between the ROM and the full-order dynamic system are often ignored. We introduce the latest results from behavioral systems theory by directly constructing a robust stepping controller using input-state data collected during flat-ground walking with a nominal controller in the simulation. The model uncertainty discrepancies are equivalently represented as bounded noise and over-approximated by bounded energy ellipsoids. We conducted extensive walking experiments in a simulation on a 22-degrees-of-freedom small humanoid robot, verifying that it demonstrates superior robustness in handling uncertain loads, various sloped terrains, and push recovery compared to the nominal S2S controller.

In this letter, we present a low-cost, easy-to-implement sim-to-real framework for biped locomotion that narrows the reality gap using only simulation data, without motion-capture or additional real-world measurements. First, a walking policy for the BRUCE robot is trained in Isaac Gym via reinforcement learning. Next, we develop a compact, physics-informed neural network (PINN) grounded in Euler-Lagrange structure and augmented with an LSTM to predict simulator forward dynamics. Trained solely on simulation trajectories, the PINN forecasts next-step joint angles and velocities of the simulated robot given the physical robot’s current state and control inputs. During hardware deployment, and consistent with a whole-body control architecture, these predicted states serve as reference joint states while the policy outputs provide feedforward torque commands; a feedforward-plus-feedback torque controller then computes the executed joint torques, thereby reducing the sim-to-real gap. Experiments on BRUCE demonstrate that our method better reproduces simulated behavior and attains higher tracking accuracy than direct policy transfer. Furthermore, the dynamics predictor runs at 1 kHz on embedded hardware, showing superior real-time performance relative to existing learning-based models.

Humans can naturally switch between low-speed walking and high-speed running. For biped robots, this demands both multigait switching capability and high-speed motion performance. Imitation learning can readily generate diverse gaits using human motion data, but it is constrained by dataset quality and dynamic discrepancies between robots and humans, hindering the achievement of robust high-speed running. To address this limitation, we forgo human data and instead adopt a hybrid linear inverted pendulum (HLIP) as a dynamics prior: the HLIP generates nominal footholds and swing-leg trajectories online and in parallel, and these references are combined with reinforcement learning to guide exploration toward high-speed, multigait behaviors that better match the robot’s own dynamics. Specifically, we abstract the robot as a linear inverted pendulum and derive unified walking and running dynamics, yielding an HLIP that captures the key features of both gaits. Based on this model, a foothold planner is designed to generate nominal footholds. Then, a foothold tracking reward, in conjunction with other task-specific reward functions, is employed to guide the robot in exploring more stable high-speed multigait behaviors. We validate our approach on the 0.7-m-tall biped BRUCE, which seamlessly switches between walking and running on varied terrains, reaching 2.5 (simulation) and 1.8 m/s (hardware) top speeds. This hardware speed substantially exceeds the reported 0.6 m/s top speed of comparable sub-1 m bipeds, demonstrating that the learned policy concurrently acquires high-speed locomotion and multigait capabilities.