This manuscript primarily aims to enhance the performance of whole-body controllers(WBC) for underactuated legged locomotion. We introduce a systematic parameter design mechanism for the floating-base feedback control within the WBC. The proposed approach involves utilizing the linearized model of unactuated dynamics to formulate a Linear Quadratic Regulator(LQR) and solving a Riccati gain while accounting for potential physical constraints through a second-order approximation of the log-barrier function. And then the user-tuned feedback gain for the floating base task is replaced by a new one constructed from the solved Riccati gain. Extensive simulations conducted in MuJoCo with a point bipedal robot, as well as real-world experiments performed on a quadruped robot, demonstrate the effectiveness of the proposed method. In the different bipedal locomotion tasks, compared with the user-tuned method, the proposed approach is at least 12% better and up to 50% better at linear velocity tracking, and at least 7% better and up to 47% better at angular velocity tracking. In the quadruped experiment, linear velocity tracking is improved by at least 3% and angular velocity tracking is improved by at least 23% using the proposed method.

This work presents a hierarchical framework for bipedal locomotion that combines a Reinforcement Learning (RL)-based high-level (HL) planner policy for the online generation of task space commands with a model-based low-level (LL) controller to track the desired task space trajectories. Different from traditional end-to-end learning approaches, our HL policy takes insights from the angular momentum-based linear inverted pendulum (ALIP) to carefully design the observation and action spaces of the Markov Decision Process (MDP). This simple yet effective design creates an insightful mapping between a low-dimensional state that effectively captures the complex dynamics of bipedal locomotion and a set of task space outputs that shape the walking gait of the robot. The HL policy is agnostic to the task space LL controller, which increases the flexibility of the design and generalization of the framework to other bipedal robots. This hierarchical design results in a learning-based framework with improved performance, data efficiency, and robustness compared with the ALIP model-based approach and state-of-the-art learning-based frameworks for bipedal locomotion. The proposed hierarchical controller is tested in three different robots, Rabbit, a five-link underactuated planar biped; Walker2D, a seven-link fully-actuated planar biped; and Digit, a 3D humanoid robot with 20 actuated joints. The trained policy naturally learns human-like locomotion behaviors and is able to effectively track a wide range of walking speeds while preserving the robustness and stability of the walking gait even under adversarial conditions.

This article studies capturability and push recovery for quadruped locomotion. Despite the rich literature on capturability analysis and push recovery for legged robots, existing tools have been developed mainly with the requirement of reaching static or quasi-static balance following a push. In practice, this requirement commonly restricts capturability analysis to cases with simple dynamics and fails to encode the time dependence of capturable states for legged locomotion with time-based gaits. To address these issues, we apply switched systems to model quadruped locomotion and extend capturability notions through a novel specification ofdynamic balance. We also provide an explicit model predictive control (EMPC) scheme to compute the dynamic balance and capturable tubes and offer a way of using the capturable tube to synthesize push recovery controllers. Such a generalization allows for a rigorous characterization of disturbance timing on the capturability of quadrupedal locomotion and opens the door of disturbance-timing-aware push recovery control strategies. Extensive simulation and hardware experiments illustrate the necessity of considering dynamic balance for quadrupedal push recovery, reveal how disturbance timing affects capturability, and demonstrate the significant improvement in disturbance rejection with the proposed strategy. Hardware experimental validations on a replica of the Mini Cheetah quadruped further verify that the proposed approach performs statistically better than the state-of-the-art baseline considered.

In this work, an advanced quadruped robot with abundant kinematic loops and passive joints is introduced. Due to the existence of many closed chains, the robot dynamic model is quite complex, and is derived using the Gauss's principle of least constraint. To explicitly consider the loop-closure constraints, we propose a task-space inverse dynamics based approach to obtain the robot locomotion controller. Besides, to meet the demand of high frequency (≥ 500Hz) in controller, an alternative method is provided. It uses the projected dynamics to find an analytical mapping from the desired contact force to the desired torque of actuators under full consideration of passive joints and loop-closure constraints. The effectiveness and efficiency of the proposed algorithms in this paper have been validated by simulation with a reliable physical engine MuJoCo.

This paper studies push recovery for humanoid robots based on a variable-height inverted pendulum (VHIP) model. We first develop an approach for treating zero-step capturability of the VHIP with a novel methodology based on Hamilton-Jacobi (HJ) reachability analysis. Such an approach uses the sub-zero level set of a value function to encode capturability of the VHIP, where the value function is obtained by numerically solving a HJ variational inequality offline. Based on this analysis, a simple and effective method for adjusting foothold locations is then devised for cases where the VHIP state is not zero-step capturable. In addition, the HJ reachability analysis naturally induces an optimal control law that allows for rapid planning with the VHIP during push recovery online. To enable use of the strategy with a position-controlled humanoid robot, an associated differential inverse kinematics based tracking controller is employed. The effectiveness of the overall framework is demonstrated with the UBTECH Walker robot in the MuJoCo simulator. Simulation validations show a significant improvement in push robustness as compared to the methods based on the classical linear inverted pendulum model.

This paper studies stabilizer design for position-controlled humanoid robots. Stabilizers are an essential part for position-controlled humanoids, whose primary objective is to adjust the control input sent to the robot to assist the tracking controller to better follow the planned reference trajectory. To achieve this goal, this paper develops a novel force-feedback based whole-body stabilizer that fully exploits the six-dimensional force measurement information and the whole-body dynamics to improve tracking performance. Relying on rigorous analysis of whole-body dynamics of position-controlled humanoids under unknown contact, the developed stabilizer leverages quadratic-programming based technique that allows cooperative consideration of both the center-of-mass tracking and contact force tracking. The effectiveness of the proposed stabilizer is demonstrated on the UBTECH Walker robot in the MuJoCo simulator. Simulation validations show a significant improvement in various scenarios as compared to commonly adopted stabilizers based on the zero-moment-point feedback and the linear inverted pendulum model.