In the context of legged robots, adaptive behavior involves adaptive balancing and adaptive swing foot reflection. While adaptive balancing counteracts perturbations to the robot, adaptive swing foot reflection helps the robot to navigate intricate terrains without foot entrapment. In this paper, we manage to bring both aspects of adaptive behavior to quadruped locomotion by combining RL and MPC while improving the robustness and agility of blind legged locomotion. This integration leverages MPC's strength in predictive capabilities and RL's adeptness in drawing from past experiences. Unlike traditional locomotion controls that separate stance foot control and swing foot trajectory, our innovative approach unifies them, addressing their lack of synchronization. At the heart of our contribution is the synthesis of stance foot control with swing foot reflection, improving agility and robustness in locomotion with adaptive behavior. A hallmark of our approach is robust blind stair climbing through swing foot reflection. Moreover, we intentionally designed the learning module as a general plugin for different robot platforms. We trained the policy and implemented our approach on the Unitree A1 robot, achieving impressive results: a peak turn rate of 8.5 rad/s, a peak running speed of 3 m/s, and steering at a speed of 2.5 m/s. Remarkably, this framework also allows the robot to maintain stable locomotion while bearing an unexpected load of 10 kg, or 83\% of its body mass. We further demonstrate the generalizability and robustness of the same policy where it realizes zero-shot transfer to different robot platforms like Go1 and AlienGo robots for load carrying. Code is made available for the use of the research community at https://github.com/DRCL-USC/RL_augmented_MPC.git

The agility of animals, particularly in complex activities such as running, turning, jumping, and backflipping, stands as an exemplar for robotic system design. Transferring this suite of behaviors to legged robotic systems introduces essential inquiries: How can a robot be trained to learn multiple locomotion behaviors simultaneously? How can the robot execute these tasks with a smooth transition? And what strategies allow for the integrated application of these skills? This paper introduces the Versatile Instructable Motion prior (VIM) - a Reinforcement Learning framework designed to incorporate a range of agile locomotion tasks suitable for advanced robotic applications. Our framework enables legged robots to learn diverse agile low-level skills by imitating animal motions and manually designed motions with Functionality reward and Stylization reward. While the Functionality reward guides the robot's ability to adopt varied skills, the Stylization reward ensures performance alignment with reference motions. Our evaluations of the VIM framework span both simulation environments and real-world deployment. To our understanding, this is the first work that allows a robot to concurrently learn diverse agile locomotion tasks using a singular controller. Further details and supportive media can be found at our project site: https://rchalyang.github.io/VIM .

Enabling robots to effectively imitate expert skills in longhorizon tasks such as locomotion, manipulation, and more, poses a long-standing challenge. Existing imitation learning (IL) approaches for robots still grapple with sub-optimal performance in complex tasks. In this paper, we consider how this challenge can be addressed within the human cognitive priors. Heuristically, we extend the usual notion of action to a dual Cognition (high-level)-Action (low-level) architecture by introducing intuitive human cognitive priors, and propose a novel skill IL framework through human-robot interaction, called Cognition-Action-based Skill Imitation Learning (CasIL), for the robotic agent to effectively cognize and imitate the critical skills from raw visual demonstrations. CasIL enables both cognition and action imitation, while high-level skill cognition explicitly guides low-level primitive actions, providing robustness and reliability to the entire skill IL process. We evaluated our method on MuJoCo and RLBench benchmarks, as well as on the obstacle avoidance and point-goal navigation tasks for quadrupedal robot locomotion. Experimental results show that our CasIL consistently achieves competitive and robust skill imitation capability compared to other counterparts in a variety of long-horizon robotic tasks.

Hybrid dynamical systems with non-linear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of such hybrid systems can still prove to be a challenging problem because it requires simultaneous reasoning about continuous state evolution and discrete mode switching. In this work, we address this problem by extending classical Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for continuous non-linear dynamics in the presence of bounded inputs and disturbances, to hybrid dynamical systems. Our framework can compute reachable sets for hybrid systems consisting of multiple discrete modes, each with its own set of non-linear continuous dynamics, discrete transitions that can be directly commanded or forced by a discrete control input, while still accounting for control bounds and adversarial disturbances in the state evolution. Along with the reachable set, the proposed framework also provides an optimal continuous and discrete controller to ensure system safety. We demonstrate our framework in simulation on an aircraft collision avoidance problem, as well as on a real-world testbed to solve the optimal mode planning problem for a quadruped with multiple gaits.

Deep reinforcement learning has emerged as a popular and powerful way to develop locomotion controllers for quadruped robots. Common approaches have largely focused on learning actions directly in joint space, or learning to modify and offset foot positions produced by trajectory generators. Both approaches typically require careful reward shaping and training for millions of time steps, and with trajectory generators introduce human bias into the resulting control policies. In this paper, we present a learning framework that leads to the natural emergence of fast and robust bounding policies for quadruped robots. The agent both selects and controls actions directly in task space to track desired velocity commands subject to environmental noise including model uncertainty and rough terrain. We observe that this framework improves sample efficiency, necessitates little reward shaping, leads to the emergence of natural gaits such as galloping and bounding, and eases the sim-to-real transfer at running speeds. Policies can be learned in only a few million time steps, even for challenging tasks of running over rough terrain with loads of over 100% of the nominal quadruped mass. Training occurs in PyBullet, and we perform a sim-to-sim transfer to Gazebo and sim-to-real transfer to the Unitree A1 hardware. For sim-to-sim, our results show the quadruped is able to run at over 4 m/s without a load, and 3.5 m/s with a 10 kg load, which is over 83% of the nominal quadruped mass. For sim-to-real, the Unitree A1 is able to bound at 2 m/s with a 5 kg load, representing 42% of the nominal quadruped mass.