Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds

State of the art quadrupedal locomotion approaches integrate Model Predictive Control (MPC) with Reinforcement Learning (RL), enabling complex motion capabilities with planning and terrain adaptive behaviors. However, they often face compounding errors over long horizons and have limited interpretability due to the absence of physical inductive biases. We address these issues by integrating Lagrangian Neural Networks (LNNs) into an RL MPC framework, enabling physically consistent dynamics learning. At deployment, our inverse dynamics infinite horizon MPC scheme avoids costly matrix inversions, improving computational efficiency by up to 4x with minimal loss of task performance. We validate our framework through multiple ablations of the proposed LNN and its variants. We show improved sample efficiency, reduced long-horizon error, and faster real time planning compared to unstructured neural dynamics. Lastly, we also test our framework on the Unitree Go1 robot to show real world viability.

VIP-Loco: A Visually Guided Infinite Horizon Planning Framework for Legged Locomotion

Perceptive locomotion for legged robots requires anticipating and adapting to complex, dynamic environments. Model Predictive Control (MPC) serves as a strong baseline, providing interpretable motion planning with constraint enforcement, but struggles with high-dimensional perceptual inputs and rapidly changing terrain. In contrast, model-free Reinforcement Learning (RL) adapts well across visually challenging scenarios but lacks planning. To bridge this gap, we propose VIP-Loco, a framework that integrates vision-based scene understanding with RL and planning. During training, an internal model maps proprioceptive states and depth images into compact kinodynamic features used by the RL policy. At deployment, the learned models are used within an infinite-horizon MPC formulation, combining adaptability with structured planning. We validate VIP-Loco in simulation on challenging locomotion tasks, including slopes, stairs, crawling, tilting, gap jumping, and climbing, across three robot morphologies: a quadruped (Unitree Go1), a biped (Cassie), and a wheeled-biped (TronA1-W). Through ablations and comparisons with state-of-the-art methods, we show that VIP-Loco unifies planning and perception, enabling robust, interpretable locomotion in diverse environments.

STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matching

Robotic systems operating in unstructured environments must operate under significant uncertainty arising from intermittent contacts, frictional variability, and unmodeled compliance. While recent model-free approaches have demonstrated impressive performance, many deployment settings still require predictive models that support planning, constraint handling, and online adaptation. Analytical rigid-body models provide strong physical structure but often fail to capture complex interaction effects, whereas purely data-driven models may violate physical consistency, exhibit data bias, and accumulate long-horizon drift. In this work, we propose STRIDE, a dynamics learning framework that explicitly separates conservative rigid-body mechanics from uncertain, effectively stochastic non-conservative interaction effects. The structured component is modeled using a Lagrangian Neural Network (LNN) to preserve energy-consistent inertial dynamics, while residual interaction forces are represented using Conditional Flow Matching (CFM) to capture multi-modal interaction phenomena. The two components are trained jointly end-to-end, enabling the model to retain physical structure while representing complex stochastic behavior. We evaluate STRIDE on systems of increasing complexity, including a pendulum, the Unitree Go1 quadruped, and the Unitree G1 humanoid. Results show 20% reduction in long-horizon prediction error and 30% reduction in contact force prediction error compared to deterministic residual baselines, supporting more reliable model-based control in uncertain robotic environments.

V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functions

Ensuring safety in autonomous systems requires controllers that satisfy hard, state-wise constraints without relying on online interaction. While existing Safe Offline RL methods typically enforce soft expected-cost constraints, they do not guarantee forward invariance. Conversely, Control Barrier Functions (CBFs) provide rigorous safety guarantees but usually depend on expert-designed barrier functions or full knowledge of the system dynamics. We introduce Value-Guided Offline Control Barrier Functions (V-OCBF), a framework that learns a neural CBF entirely from offline demonstrations. Unlike prior approaches, V-OCBF does not assume access to the dynamics model; instead, it derives a recursive finite-difference barrier update, enabling model-free learning of a barrier that propagates safety information over time. Moreover, V-OCBF incorporates an expectile-based objective that avoids querying the barrier on out-of-distribution actions and restricts updates to the dataset-supported action set. The learned barrier is then used with a Quadratic Program (QP) formulation to synthesize real-time safe control. Across multiple case studies, V-OCBF yields substantially fewer safety violations than baseline methods while maintaining strong task performance, highlighting its scalability for offline synthesis of safety-critical controllers without online interaction or hand-engineered barriers.

Real-Time Gait Adaptation for Quadrupeds using Model Predictive Control and Reinforcement Learning

Model-free reinforcement learning (RL) has enabled adaptable and agile quadruped locomotion; however, policies often converge to a single gait, leading to suboptimal performance. Traditionally, Model Predictive Control (MPC) has been extensively used to obtain task-specific optimal policies but lacks the ability to adapt to varying environments. To address these limitations, we propose an optimization framework for real-time gait adaptation in a continuous gait space, combining the Model Predictive Path Integral (MPPI) algorithm with a Dreamer module to produce adaptive and optimal policies for quadruped locomotion. At each time step, MPPI jointly optimizes the actions and gait variables using a learned Dreamer reward that promotes velocity tracking, energy efficiency, stability, and smooth transitions, while penalizing abrupt gait changes. A learned value function is incorporated as terminal reward, extending the formulation to an infinite-horizon planner. We evaluate our framework in simulation on the Unitree Go1, demonstrating an average reduction of up to 36.48\% in energy consumption across varying target speeds, while maintaining accurate tracking and adaptive, task-appropriate gaits.

COMPAct: Computational Optimization and Automated Modular design of Planetary Actuators

The optimal design of robotic actuators is a critical area of research, yet limited attention has been given to optimizing gearbox parameters and automating actuator CAD. This paper introduces COMPAct: Computational Optimization and Automated Modular Design of Planetary Actuators, a framework that systematically identifies optimal gearbox parameters for a given motor across four gearbox types, single-stage planetary gearbox (SSPG), compound planetary gearbox (CPG), Wolfrom planetary gearbox (WPG), and double-stage planetary gearbox (DSPG). The framework minimizes mass and actuator width while maximizing efficiency, and further automates actuator CAD generation to enable direct 3D printing without manual redesign. Using this framework, optimal gearbox designs are explored over a wide range of gear ratios, providing insights into the suitability of different gearbox types across various gear ratio ranges. In addition, the framework is used to generate CAD models of all four gearbox types with varying gear ratios and motors. Two actuator types are fabricated and experimentally evaluated through power efficiency, no-load backlash, and transmission stiffness tests. Experimental results indicate that the SSPG actuator achieves a mechanical efficiency of 60-80 %, a no-load backlash of 0.59 deg, and a transmission stiffness of 242.7 Nm/rad, while the CPG actuator demonstrates 60 % efficiency, 2.6 deg backlash, and a stiffness of 201.6 Nm/rad. Code available at: https://anonymous.4open.science/r/COMPAct-SubNum-3408 Video: https://youtu.be/99zOKgxsDho

Signal Temporal Logic Compliant Co-design of Planning and Control

This work presents a novel co-design strategy that integrates trajectory planning and control to handle STL-based tasks in autonomous robots. The method consists of two phases: $(i)$ learning spatio-temporal motion primitives to encapsulate the inherent robot-specific constraints and $(ii)$ constructing an STL-compliant motion plan from these primitives. Initially, we employ reinforcement learning to construct a library of control policies that perform trajectories described by the motion primitives. Then, we map motion primitives to spatio-temporal characteristics. Subsequently, we present a sampling-based STL-compliant motion planning strategy tailored to meet the STL specification. The proposed model-free approach, which generates feasible STL-compliant motion plans across various environments, is validated on differential-drive and quadruped robots across various STL specifications. Demonstration videos are available at https://tinyurl.com/m6zp7rsm.

GROQLoco: Generalist and RObot-agnostic Quadruped Locomotion Control using Offline Datasets

Recent advancements in large-scale offline training have demonstrated the potential of generalist policy learning for complex robotic tasks. However, applying these principles to legged locomotion remains a challenge due to continuous dynamics and the need for real-time adaptation across diverse terrains and robot morphologies. In this work, we propose GROQLoco, a scalable, attention-based framework that learns a single generalist locomotion policy across multiple quadruped robots and terrains, relying solely on offline datasets. Our approach leverages expert demonstrations from two distinct locomotion behaviors - stair traversal (non-periodic gaits) and flat terrain traversal (periodic gaits) - collected across multiple quadruped robots, to train a generalist model that enables behavior fusion for both behaviors. Crucially, our framework operates directly on proprioceptive data from all robots without incorporating any robot-specific encodings. The policy is directly deployable on an Intel i7 nuc, producing low-latency control outputs without any test-time optimization. Our extensive experiments demonstrate strong zero-shot transfer across highly diverse quadruped robots and terrains, including hardware deployment on the Unitree Go1, a commercially available 12kg robot. Notably, we evaluate challenging cross-robot training setups where different locomotion skills are unevenly distributed across robots, yet observe successful transfer of both flat walking and stair traversal behaviors to all robots at test time. We also show preliminary walking on Stoch 5, a 70kg quadruped, on flat and outdoor terrains without requiring any fine tuning. These results highlight the potential for robust generalist locomotion across diverse robots and terrains.

MULE: Multi-terrain and Unknown Load Adaptation for Effective Quadrupedal Locomotion

Quadrupedal robots are increasingly deployed for load-carrying tasks across diverse terrains. While Model Predictive Control (MPC)-based methods can account for payload variations, they often depend on predefined gait schedules or trajectory generators, limiting their adaptability in unstructured environments. To address these limitations, we propose an Adaptive Reinforcement Learning (RL) framework that enables quadrupedal robots to dynamically adapt to both varying payloads and diverse terrains. The framework consists of a nominal policy responsible for baseline locomotion and an adaptive policy that learns corrective actions to preserve stability and improve command tracking under payload variations. We validate the proposed approach through large-scale simulation experiments in Isaac Gym and real-world hardware deployment on a Unitree Go1 quadruped. The controller was tested on flat ground, slopes, and stairs under both static and dynamic payload changes. Across all settings, our adaptive controller consistently outperformed the controller in tracking body height and velocity commands, demonstrating enhanced robustness and adaptability without requiring explicit gait design or manual tuning.

Neural Control Barrier Functions from Physics Informed Neural Networks

As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific applications remains a significant challenge. With the advent of deep learning techniques, recent research has explored synthesizing CBFs using neural networks-commonly referred to as neural CBFs. This paper introduces a novel class of neural CBFs that leverages a physics-inspired neural network framework by incorporating Zubov's Partial Differential Equation (PDE) within the context of safety. This approach provides a scalable methodology for synthesizing neural CBFs applicable to high-dimensional systems. Furthermore, by utilizing reciprocal CBFs instead of zeroing CBFs, the proposed framework allows for the specification of flexible, user-defined safe regions. To validate the effectiveness of the approach, we present case studies on three different systems: an inverted pendulum, autonomous ground navigation, and aerial navigation in obstacle-laden environments.