Long-horizon Locomotion and Manipulation on a Quadrupedal Robot with Large Language Models

We present a large language model (LLM) based system to empower quadrupedal robots with problem-solving abilities for long-horizon tasks beyond short-term motions. Long-horizon tasks for quadrupeds are challenging since they require both a high-level understanding of the semantics of the problem for task planning and a broad range of locomotion and manipulation skills to interact with the environment. Our system builds a high-level reasoning layer with large language models, which generates hybrid discrete-continuous plans as robot code from task descriptions. It comprises multiple LLM agents: a semantic planner for sketching a plan, a parameter calculator for predicting arguments in the plan, and a code generator to convert the plan into executable robot code. At the low level, we adopt reinforcement learning to train a set of motion planning and control skills to unleash the flexibility of quadrupeds for rich environment interactions. Our system is tested on long-horizon tasks that are infeasible to complete with one single skill. Simulation and real-world experiments show that it successfully figures out multi-step strategies and demonstrates non-trivial behaviors, including building tools or notifying a human for help.

Learning Visual Quadrupedal Loco-Manipulation from Demonstrations

Quadruped robots are progressively being integrated into human environments. Despite the growing locomotion capabilities of quadrupedal robots, their interaction with objects in realistic scenes is still limited. While additional robotic arms on quadrupedal robots enable manipulating objects, they are sometimes redundant given that a quadruped robot is essentially a mobile unit equipped with four limbs, each possessing 3 degrees of freedom (DoFs). Hence, we aim to empower a quadruped robot to execute real-world manipulation tasks using only its legs. We decompose the loco-manipulation process into a low-level reinforcement learning (RL)-based controller and a high-level Behavior Cloning (BC)-based planner. By parameterizing the manipulation trajectory, we synchronize the efforts of the upper and lower layers, thereby leveraging the advantages of both RL and BC. Our approach is validated through simulations and real-world experiments, demonstrating the robot's ability to perform tasks that demand mobility and high precision, such as lifting a basket from the ground while moving, closing a dishwasher, pressing a button, and pushing a door. Project website: https://zhengmaohe.github.io/leg-manip

Adaptive Energy Regularization for Autonomous Gait Transition and Energy-Efficient Quadruped Locomotion

In reinforcement learning for legged robot locomotion, crafting effective reward strategies is crucial. Pre-defined gait patterns and complex reward systems are widely used to stabilize policy training. Drawing from the natural locomotion behaviors of humans and animals, which adapt their gaits to minimize energy consumption, we propose a simplified, energy-centric reward strategy to foster the development of energy-efficient locomotion across various speeds in quadruped robots. By implementing an adaptive energy reward function and adjusting the weights based on velocity, we demonstrate that our approach enables ANYmal-C and Unitree Go1 robots to autonomously select appropriate gaits, such as four-beat walking at lower speeds and trotting at higher speeds, resulting in improved energy efficiency and stable velocity tracking compared to previous methods using complex reward designs and prior gait knowledge. The effectiveness of our policy is validated through simulations in the IsaacGym simulation environment and on real robots, demonstrating its potential to facilitate stable and adaptive locomotion.

Leveraging Symmetry in RL-based Legged Locomotion Control

Model-free reinforcement learning is a promising approach for autonomously solving challenging robotics control problems, but faces exploration difficulty without information of the robot's kinematics and dynamics morphology. The under-exploration of multiple modalities with symmetric states leads to behaviors that are often unnatural and sub-optimal. This issue becomes particularly pronounced in the context of robotic systems with morphological symmetries, such as legged robots for which the resulting asymmetric and aperiodic behaviors compromise performance, robustness, and transferability to real hardware. To mitigate this challenge, we can leverage symmetry to guide and improve the exploration in policy learning via equivariance/invariance constraints. In this paper, we investigate the efficacy of two approaches to incorporate symmetry: modifying the network architectures to be strictly equivariant/invariant, and leveraging data augmentation to approximate equivariant/invariant actor-critics. We implement the methods on challenging loco-manipulation and bipedal locomotion tasks and compare with an unconstrained baseline. We find that the strictly equivariant policy consistently outperforms other methods in sample efficiency and task performance in simulation. In addition, symmetry-incorporated approaches exhibit better gait quality, higher robustness and can be deployed zero-shot in real-world experiments.

Humanoid Locomotion as Next Token Prediction

We cast real-world humanoid control as a next token prediction problem, akin to predicting the next word in language. Our model is a causal transformer trained via autoregressive prediction of sensorimotor trajectories. To account for the multi-modal nature of the data, we perform prediction in a modality-aligned way, and for each input token predict the next token from the same modality. This general formulation enables us to leverage data with missing modalities, like video trajectories without actions. We train our model on a collection of simulated trajectories coming from prior neural network policies, model-based controllers, motion capture data, and YouTube videos of humans. We show that our model enables a full-sized humanoid to walk in San Francisco zero-shot. Our model can transfer to the real world even when trained on only 27 hours of walking data, and can generalize to commands not seen during training like walking backward. These findings suggest a promising path toward learning challenging real-world control tasks by generative modeling of sensorimotor trajectories.

Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes

Learning-based approaches are emerging as an effective approach for safety filters for black-box dynamical systems. Existing methods have relied on certificate functions like Control Barrier Functions (CBFs) and Hamilton-Jacobi (HJ) reachability value functions. The primary motivation for our work is the recognition that ultimately, enforcing the safety constraint as a control input constraint at each state is what matters. By focusing on this constraint, we can eliminate dependence on any specific certificate function-based design. To achieve this, we define a discriminating hyperplane that shapes the half-space constraint on control input at each state, serving as a sufficient condition for safety. This concept not only generalizes over traditional safety methods but also simplifies safety filter design by eliminating dependence on specific certificate functions. We present two strategies to learn the discriminating hyperplane: (a) a supervised learning approach, using pre-verified control invariant sets for labeling, and (b) a reinforcement learning (RL) approach, which does not require such labels. The main advantage of our method, unlike conventional safe RL approaches, is the separation of performance and safety. This offers a reusable safety filter for learning new tasks, avoiding the need to retrain from scratch. As such, we believe that the new notion of the discriminating hyperplane offers a more generalizable direction towards designing safety filters, encompassing and extending existing certificate-function-based or safe RL methodologies.

Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control

This paper presents a comprehensive study on using deep reinforcement learning (RL) to create dynamic locomotion controllers for bipedal robots. Going beyond focusing on a single locomotion skill, we develop a general control solution that can be used for a range of dynamic bipedal skills, from periodic walking and running to aperiodic jumping and standing. Our RL-based controller incorporates a novel dual-history architecture, utilizing both a long-term and short-term input/output (I/O) history of the robot. This control architecture, when trained through the proposed end-to-end RL approach, consistently outperforms other methods across a diverse range of skills in both simulation and the real world.The study also delves into the adaptivity and robustness introduced by the proposed RL system in developing locomotion controllers. We demonstrate that the proposed architecture can adapt to both time-invariant dynamics shifts and time-variant changes, such as contact events, by effectively using the robot's I/O history. Additionally, we identify task randomization as another key source of robustness, fostering better task generalization and compliance to disturbances. The resulting control policies can be successfully deployed on Cassie, a torque-controlled human-sized bipedal robot. This work pushes the limits of agility for bipedal robots through extensive real-world experiments. We demonstrate a diverse range of locomotion skills, including: robust standing, versatile walking, fast running with a demonstration of a 400-meter dash, and a diverse set of jumping skills, such as standing long jumps and high jumps.

Constraint-Guided Online Data Selection for Scalable Data-Driven Safety Filters in Uncertain Robotic Systems

As the use of autonomous robotic systems expands in tasks that are complex and challenging to model, the demand for robust data-driven control methods that can certify safety and stability in uncertain conditions is increasing. However, the practical implementation of these methods often faces scalability issues due to the growing amount of data points with system complexity, and a significant reliance on high-quality training data. In response to these challenges, this study presents a scalable data-driven controller that efficiently identifies and infers from the most informative data points for implementing data-driven safety filters. Our approach is grounded in the integration of a model-based certificate function-based method and Gaussian Process (GP) regression, reinforced by a novel online data selection algorithm that reduces time complexity from quadratic to linear relative to dataset size. Empirical evidence, gathered from successful real-world cart-pole swing-up experiments and simulated locomotion of a five-link bipedal robot, demonstrates the efficacy of our approach. Our findings reveal that our efficient online data selection algorithm, which strategically selects key data points, enhances the practicality and efficiency of data-driven certifying filters in complex robotic systems, significantly mitigating scalability concerns inherent in nonparametric learning-based control methods.

Prompt a Robot to Walk with Large Language Models

Large language models (LLMs) pre-trained on vast internet-scale data have showcased remarkable capabilities across diverse domains. Recently, there has been escalating interest in deploying LLMs for robotics, aiming to harness the power of foundation models in real-world settings. However, this approach faces significant challenges, particularly in grounding these models in the physical world and in generating dynamic robot motions. To address these issues, we introduce a novel paradigm in which we use few-shot prompts collected from the physical environment, enabling the LLM to autoregressively generate low-level control commands for robots without task-specific fine-tuning. Experiments across various robots and environments validate that our method can effectively prompt a robot to walk. We thus illustrate how LLMs can proficiently function as low-level feedback controllers for dynamic motion control even in high-dimensional robotic systems. The project website and source code can be found at: https://prompt2walk.github.io/ .

Nonsmooth Control Barrier Functions for Obstacle Avoidance between Convex Regions

In this paper, we focus on non-conservative obstacle avoidance between robots with control affine dynamics with strictly convex and polytopic shapes. The core challenge for this obstacle avoidance problem is that the minimum distance between strictly convex regions or polytopes is generally implicit and non-smooth, such that distance constraints cannot be enforced directly in the optimization problem. To handle this challenge, we employ non-smooth control barrier functions to reformulate the avoidance problem in the dual space, with the positivity of the minimum distance between robots equivalently expressed using a quadratic program. Our approach is proven to guarantee system safety. We theoretically analyze the smoothness properties of the minimum distance quadratic program and its KKT conditions. We validate our approach by demonstrating computationally-efficient obstacle avoidance for multi-agent robotic systems with strictly convex and polytopic shapes. To our best knowledge, this is the first time a real-time QP problem can be formulated for general non-conservative avoidance between strictly convex shapes and polytopes.