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This paper presents a novel framework for learning robust bipedal walking by combining a data-driven state representation with a Reinforcement Learning (RL) based locomotion policy. The framework utilizes an autoencoder to learn a low-dimensional latent space that captures the complex dynamics of bipedal locomotion from existing locomotion data. This reduced dimensional state representation is then used as states for training a robust RL-based gait policy, eliminating the need for heuristic state selections or the use of template models for gait planning. The results demonstrate that the learned latent variables are disentangled and directly correspond to different gaits or speeds, such as moving forward, backward, or walking in place. Compared to traditional template model-based approaches, our framework exhibits superior performance and robustness in simulation. The trained policy effectively tracks a wide range of walking speeds and demonstrates good generalization capabilities to unseen scenarios. 

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. 

Linear policies are the simplest class of policies that can achieve stable bipedal walking behaviors in both simulation and hardware. However, a significant challenge in deploying them widely is the difficulty in extending them to more dynamic behaviors like hopping and running. Therefore, in this work, we propose a new class of linear policies in which template models can be embedded. In particular, we show how to embed Spring Loaded Inverted Pendulum (SLIP) model in the policy class and realize perpetual hopping in arbitrary directions. The spring constant of the template model is learned in addition to the remaining parameters of the policy. Given this spring constant, the goal is to realize hopping trajectories using the SLIP model, which are then tracked by the bipedal robot using the linear policy. Continuous hopping with adjustable heading direction was achieved across different terrains in simulation with heading and lateral velocities of up to O.5m/ sec and 0.05m/ sec, respectively. The policy was then transferred to the hardware, and preliminary results (> 10 steps) of hopping were achieved. 

This article studies the class of scenario-based safety testing algorithms in the black-box safety testing configuration. For algorithms sharing the same state–action set coverage with different sampling distributions, it is commonly believed that prioritizing the exploration of high-risk states and actions leads to a better sampling efficiency. Our proposal disputes the above intuition by introducing an impossibility theorem that provably shows that all the safety testing algorithms of the aforementioned difference perform equally well with the same expected sampling efficiency. Moreover, for testing algorithms covering different sets of states and actions, the sampling efficiency criterion is no longer applicable as different algorithms do not necessarily converge to the same termination condition. We then propose a testing aggressiveness definition based on the almost safe set concept along with an unbiased and efficient algorithm that compares the aggressiveness between testing algorithms. Empirical observations from the safety testing of bipedal locomotion controllers and vehicle decision-making modules are also presented to support the proposed theoretical implications and methodologies. 

Controller design for bipedal walking on dynamic rigid surfaces (DRSes), which are rigid surfaces moving in the inertial frame (e.g., ships and airplanes), remains largely underexplored. This paper introduces a hierarchical control approach that achieves stable underactuated bipedal walking on a horizontally oscillating DRS. The highest layer of our approach is a real-time motion planner that generates desired global behaviors (i.e., center of mass trajectories and footstep locations) by stabilizing a reduced-order robot model. One key novelty of this layer is the derivation of the reduced-order model by analytically extending the angular momentum based linear inverted pendulum (ALIP) model from stationary to horizontally moving surfaces. The other novelty is the development of a discrete-time foot-placement controller that exponentially stabilizes the hybrid, linear, time-varying ALIP. The middle layer translates the desired global behaviors into the robot’s full-body reference trajectories for all directly actuated degrees of freedom, while the lowest layer exponentially tracks those reference trajectories based on the full-order, hybrid, nonlinear robot model. Simulations confirm that the proposed framework ensures stable walking of a planar underactuated biped under different swaying DRS motions and gait types. 

Safe path planning is critical for bipedal robots to operate in safety-critical environments. Common path planning algorithms, such as RRT or RRT*, typically use geometric or kinematic collision check algorithms to ensure collision-free paths toward the target position. However, such approaches may generate non-smooth paths that do not comply with the dynamics constraints of walking robots. It has been shown that the control barrier function (CBF) can be integrated with RRT/RRT* to synthesize dynamically feasible collision-free paths. Yet, existing work has been limited to simple circular or elliptical shape obstacles due to the challenging nature of constructing appropriate barrier functions to represent irregularly shaped obstacles. In this paper, we present a CBF-based RRT* algorithm for bipedal robots to generate a collision-free path through space with multiple polynomial-shaped obstacles. In particular, we used logistic regression to construct polynomial barrier functions from a grid map of the environment to represent irregularly shaped obstacles. Moreover, we developed a multi-step CBF steering controller to ensure the efficiency of free space exploration. The proposed approach was first validated in simulation for a differential drive model, and then experimentally evaluated with a 3D humanoid robot, Digit, in a lab setting with randomly placed obstacles. 

We present a framework to generate periodic trajectory references for a 3D under-actuated bipedal robot, using a linear inverted pendulum (LIP) based controller with adaptive neural regulation. We use the LIP template model to estimate the robot's center of mass (CoM) position and velocity at the end of the current step, and formulate a discrete controller that determines the next footstep location to achieve a desired walking profile. This controller is equipped on the frontal plane with a Neural-Network-based adaptive term that reduces the model mismatch between the template and physical robot that particularly affects the lateral motion. Then, the foot placement location computed for the LIP model is used to generate task space trajectories (CoM and swing foot trajectories) for the actual robot to realize stable walking. We use a fast, real-time QP-based inverse kinematics algorithm that produces joint references from the task space trajectories, which makes the formulation independent of the knowledge of the robot dynamics. Finally, we implemented and evaluated the proposed approach in simulation and hardware experiments with a Digit robot obtaining stable periodic locomotion for both cases. 

The dynamic response of the legged robot locomotion is non-Lipschitz and can be stochastic due to environmental uncertainties. To test, validate, and characterize the safety performance of legged robots, existing solutions on observed and inferred risk can be incomplete and sampling inefficient. Some formal verification methods suffer from the model precision and other surrogate assumptions. In this paper, we propose a scenario sampling based testing framework that characterizes the overall safety performance of a legged robot by specifying (i) where (in terms of a set of states) the robot is potentially safe, and (ii) how safe the robot is within the specified set. The framework can also help certify the commercial deployment of the legged robot in real-world environment along with human and compare safety performance among legged robots with different mechanical structures and dynamic properties. The proposed framework is further deployed to evaluate a group of state-of-the-art legged robot locomotion controllers from various model-based, deep neural network involved, and reinforcement learning based methods in the literature. Among a series of intended work domains of the studied legged robots (e.g. tracking speed on sloped surface, with abrupt changes on demanded velocity, and against adversarial push-over disturbances), we show that the method can adequately capture the overall safety characterization and the subtle performance insights. Many of the observed safety outcomes, to the best of our knowledge, have never been reported by the existing work in the legged robot literature.