Yao Lyu

Zuxing Lu, Ziang Zheng, Yao Lyu et al.

Building a general-purpose whole-body controller is essential for enabling diverse motion capabilities in humanoid robots across a wide range of downstream tasks, including locomotion and loco-manipulation. Different tasks rely on distinct motion reference modalities: locomotion primarily depends on coordinated robot joint trajectories, whereas manipulation requires precise end-effector trajectory tracking. Existing methods often overlook the representational mismatch between dense robot joint angles and sparse end-effector poses. To address this, we propose Multi-Modal Mimic (M3imic), a versatile multi-modal whole-body control framework that unifies heterogeneous motion reference modalities, including robot joint angles, human pose trajectories, and end-effector poses, using modality-specific encoders to map them into a shared latent space. Leveraging large-scale reinforcement learning in the simulator, we train a single policy that achieves sim-to-real transfer across multiple motion reference modalities without modality-specific retraining. Extensive simulation and real-world experiments on the Unitree G1 robot are conducted to evaluate the proposed framework. In simulation, the policy achieves a peak success rate of 98.42\% on an unseen test dataset, demonstrating its exceptional generalization capability. The code is available at https://github.com/Renforce-Dynamics/MultiModalWBC

Wei Wu, Honglin Chen, Wenhan Cao et al.

Tightly coupled SLAM formulations under mixed-rate sensing often bind temporal processing, local geometric association, estimator formulation, and map-update policy into method-specific designs. Such binding makes it difficult to vary one design choice without re-engineering the rest of the state-estimation process. This paper presents FUSE, a framework for unified state estimation in robotic SLAM systems. FUSE organizes the state-estimation interface around observation ingestion, propagation, update, and state query, and uses this interface to separate temporal processing, residual-ready local geometric association, estimator formulation, and map-update policy. A LiDAR--IMU instantiation is developed to examine the framework under mixed-rate sensing and directional degeneracy, where high-rate inertial propagation, LiDAR-triggered geometric update, residual screening, and degeneracy-aware correction operate through the same interface boundaries. On a 418 m loop-corridor sequence, the instantiation reports a 1.626~m end-to-end trajectory error, corresponding to a 7.9% relative error reduction compared with Faster-LIO, the lowest-error baseline on this sequence. The results support FUSE as a framework for organizing state-estimation design choices and show how the evaluated instantiation regularizes updates along weakly observable directions.

Chang Liu, Wenhan Cao, Zeju Sun et al.

Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable approximations,with Gaussian filters such as the extended and unscented Kalman filters being among the most widely used methods. This tutorial revisits Gaussian filtering from an information-geometric perspective, viewing the prediction and measurement update steps as inference procedures over state distributions. Within this framework, we introduce a geometry-aware Gaussian filtering approach that leverages natural gradient descent on the statistical manifold of Gaussian distributions. The resulting Natural Gradient Gaussian Approximation (NANO) filter iteratively refines the posterior mean and covariance while respecting the intrinsic geometry of the Gaussian family and preserving the positive definiteness of the covariance matrix. We further highlight fundamental connections to the classical Kalman filtering, showing that a single natural-gradient step exactly recovers the Kalman measurement update in the linear-Gaussian case. The practical implications of the proposed framework are illustrated through case studies in representative nonlinear estimation problems,including satellite attitude estimation, simultaneous localization and mapping, and state estimation for robotic systems including quadruped and humanoid robots.

Tianqi Zhang, Puzhen Yuan, Guojian Zhan et al.

Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal evolution of a feedback control system. Classical constrained optimization methods, such as penalty and Lagrangian approaches, inherently use proportional and integral feedback controllers. In this paper, we propose a more generic equivalence framework to build the connection between constrained optimization and feedback control system, for the purpose of developing more effective constrained RL algorithms. Firstly, we define that each step of the system evolution determines the Lagrange multiplier by solving a multiplier feedback optimal control problem (MFOCP). In this problem, the control input is multiplier, the state is policy parameters, the dynamics is described by policy gradient descent, and the objective is to minimize constraint violations. Then, we introduce a multiplier guided policy learning (MGPL) module to perform policy parameters updating. And we prove that the resulting optimal policy, achieved through alternating MFOCP and MGPL, aligns with the solution of the primal constrained RL problem, thereby establishing our equivalence framework. Furthermore, we point out that the existing PID Lagrangian is merely one special case within our framework that utilizes a PID controller. We also accommodate the integration of other various feedback controllers, thereby facilitating the development of new algorithms. As a representative, we employ model predictive control (MPC) as the feedback controller and consequently propose a new algorithm called predictive Lagrangian optimization (PLO). Numerical experiments demonstrate its superiority over the PID Lagrangian method, achieving a larger feasible region up to 7.2% and a comparable average reward.

Yao Lyu, Xiangteng Zhang, Shengbo Eben Li et al.

Training deep reinforcement learning (RL) agents necessitates overcoming the highly unstable nonconvex stochastic optimization inherent in the trial-and-error mechanism. To tackle this challenge, we propose a physics-inspired optimization algorithm called relativistic adaptive gradient descent (RAD), which enhances long-term training stability. By conceptualizing neural network (NN) training as the evolution of a conformal Hamiltonian system, we present a universal framework for transferring long-term stability from conformal symplectic integrators to iterative NN updating rules, where the choice of kinetic energy governs the dynamical properties of resulting optimization algorithms. By utilizing relativistic kinetic energy, RAD incorporates principles from special relativity and limits parameter updates below a finite speed, effectively mitigating abnormal gradient influences. Additionally, RAD models NN optimization as the evolution of a multi-particle system where each trainable parameter acts as an independent particle with an individual adaptive learning rate. We prove RAD's sublinear convergence under general nonconvex settings, where smaller gradient variance and larger batch sizes contribute to tighter convergence. Notably, RAD degrades to the well-known adaptive moment estimation (ADAM) algorithm when its speed coefficient is chosen as one and symplectic factor as a small positive value. Experimental results show RAD outperforming nine baseline optimizers with five RL algorithms across twelve environments, including standard benchmarks and challenging scenarios. Notably, RAD achieves up to a 155.1% performance improvement over ADAM in Atari games, showcasing its efficacy in stabilizing and accelerating RL training.

Ziang Zheng, Guojian Zhan, Shiqi Liu et al.

Reinforcement learning (RL) has shown great potential in enabling quadruped robots to perform agile locomotion. However, directly training policies to simultaneously handle dual extreme challenges, i.e., extreme underactuation and extreme terrains, as in monopedal hopping tasks, remains highly challenging due to unstable early-stage interactions and unreliable reward feedback. To address this, we propose JumpER (jump-start reinforcement learning via self-evolving priors), an RL training framework that structures policy learning into multiple stages of increasing complexity. By dynamically generating self-evolving priors through iterative bootstrapping of previously learned policies, JumpER progressively refines and enhances guidance, thereby stabilizing exploration and policy optimization without relying on external expert priors or handcrafted reward shaping. Specifically, when integrated with a structured three-stage curriculum that incrementally evolves action modality, observation space, and task objective, JumpER enables quadruped robots to achieve robust monopedal hopping on unpredictable terrains for the first time. Remarkably, the resulting policy effectively handles challenging scenarios that traditional methods struggle to conquer, including wide gaps up to 60 cm, irregularly spaced stairs, and stepping stones with distances varying from 15 cm to 35 cm. JumpER thus provides a principled and scalable approach for addressing locomotion tasks under the dual challenges of extreme underactuation and extreme terrains.