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Dexterous Legged Locomotion in Confined 3D Spaces with Reinforcement Learning

Recent advances of locomotion controllers utilizing deep reinforcement learning (RL) have yielded impressive results in terms of achieving rapid and robust locomotion across challenging terrain, such as rugged rocks, non-rigid ground, and slippery surfaces. However, while these controllers primarily address challenges underneath the robot, relatively little research has investigated legged mobility through confined 3D spaces, such as narrow tunnels or irregular voids, which impose all-around constraints. The cyclic gait patterns resulted from existing RL-based methods to learn parameterized locomotion skills characterized by motion parameters, such as velocity and body height, may not be adequate to navigate robots through challenging confined 3D spaces, requiring both agile 3D obstacle avoidance and robust legged locomotion. Instead, we propose to learn locomotion skills end-to-end from goal-oriented navigation in confined 3D spaces. To address the inefficiency of tracking distant navigation goals, we introduce a hierarchical locomotion controller that combines a classical planner tasked with planning waypoints to reach a faraway global goal location, and an RL-based policy trained to follow these waypoints by generating low-level motion commands. This approach allows the policy to explore its own locomotion skills within the entire solution space and facilitates smooth transitions between local goals, enabling long-term navigation towards distant goals. In simulation, our hierarchical approach succeeds at navigating through demanding confined 3D environments, outperforming both pure end-to-end learning approaches and parameterized locomotion skills. We further demonstrate the successful real-world deployment of our simulation-trained controller on a real robot.

Hybrid Internal Model: A Simple and Efficient Learner for Agile Legged Locomotion

Robust locomotion control depends on accurate state estimations. However, the sensors of most legged robots can only provide partial and noisy observations, making the estimation particularly challenging, especially for external states like terrain frictions and elevation maps. Inspired by the classical Internal Model Control principle, we consider these external states as disturbances and introduce Hybrid Internal Model (HIM) to estimate them according to the response of the robot. The response, which we refer to as the hybrid internal embedding, contains the robot's explicit velocity and implicit stability representation, corresponding to two primary goals for locomotion tasks: explicitly tracking velocity and implicitly maintaining stability. We use contrastive learning to optimize the embedding to be close to the robot's successor state, in which the response is naturally embedded. HIM has several appealing benefits: It only needs the robot's proprioceptions, i.e., those from joint encoders and IMU as observations. It innovatively maintains consistent observations between simulation reference and reality that avoids information loss in mimicking learning. It exploits batch-level information that is more robust to noises and keeps better sample efficiency. It only requires 1 hour of training on an RTX 4090 to enable a quadruped robot to traverse any terrain under any disturbances. A wealth of real-world experiments demonstrates its agility, even in high-difficulty tasks and cases never occurred during the training process, revealing remarkable open-world generalizability.

Learning H-Infinity Locomotion Control

Stable locomotion in precipitous environments is an essential capability of quadruped robots, demanding the ability to resist various external disturbances. However, recent learning-based policies only use basic domain randomization to improve the robustness of learned policies, which cannot guarantee that the robot has adequate disturbance resistance capabilities. In this paper, we propose to model the learning process as an adversarial interaction between the actor and a newly introduced disturber and ensure their optimization with H_{infty} constraint. In contrast to the actor that maximizes the discounted overall reward, the disturber is responsible for generating effective external forces and is optimized by maximizing the error between the task reward and its oracle, i.e., "cost" in each iteration. To keep joint optimization between the actor and the disturber stable, our H_{infty} constraint mandates the bound of ratio between the cost to the intensity of the external forces. Through reciprocal interaction throughout the training phase, the actor can acquire the capability to navigate increasingly complex physical disturbances. We verify the robustness of our approach on quadrupedal locomotion tasks with Unitree Aliengo robot, and also a more challenging task with Unitree A1 robot, where the quadruped is expected to perform locomotion merely on its hind legs as if it is a bipedal robot. The simulated quantitative results show improvement against baselines, demonstrating the effectiveness of the method and each design choice. On the other hand, real-robot experiments qualitatively exhibit how robust the policy is when interfering with various disturbances on various terrains, including stairs, high platforms, slopes, and slippery terrains. All code, checkpoints, and real-world deployment guidance will be made public.

Barkour: Benchmarking Animal-level Agility with Quadruped Robots

Animals have evolved various agile locomotion strategies, such as sprinting, leaping, and jumping. There is a growing interest in developing legged robots that move like their biological counterparts and show various agile skills to navigate complex environments quickly. Despite the interest, the field lacks systematic benchmarks to measure the performance of control policies and hardware in agility. We introduce the Barkour benchmark, an obstacle course to quantify agility for legged robots. Inspired by dog agility competitions, it consists of diverse obstacles and a time based scoring mechanism. This encourages researchers to develop controllers that not only move fast, but do so in a controllable and versatile way. To set strong baselines, we present two methods for tackling the benchmark. In the first approach, we train specialist locomotion skills using on-policy reinforcement learning methods and combine them with a high-level navigation controller. In the second approach, we distill the specialist skills into a Transformer-based generalist locomotion policy, named Locomotion-Transformer, that can handle various terrains and adjust the robot's gait based on the perceived environment and robot states. Using a custom-built quadruped robot, we demonstrate that our method can complete the course at half the speed of a dog. We hope that our work represents a step towards creating controllers that enable robots to reach animal-level agility.

Learning Getting-Up Policies for Real-World Humanoid Robots

Automatic fall recovery is a crucial prerequisite before humanoid robots can be reliably deployed. Hand-designing controllers for getting up is difficult because of the varied configurations a humanoid can end up in after a fall and the challenging terrains humanoid robots are expected to operate on. This paper develops a learning framework to produce controllers that enable humanoid robots to get up from varying configurations on varying terrains. Unlike previous successful applications of humanoid locomotion learning, the getting-up task involves complex contact patterns, which necessitates accurately modeling the collision geometry and sparser rewards. We address these challenges through a two-phase approach that follows a curriculum. The first stage focuses on discovering a good getting-up trajectory under minimal constraints on smoothness or speed / torque limits. The second stage then refines the discovered motions into deployable (i.e. smooth and slow) motions that are robust to variations in initial configuration and terrains. We find these innovations enable a real-world G1 humanoid robot to get up from two main situations that we considered: a) lying face up and b) lying face down, both tested on flat, deformable, slippery surfaces and slopes (e.g., sloppy grass and snowfield). To the best of our knowledge, this is the first successful demonstration of learned getting-up policies for human-sized humanoid robots in the real world. Project page: https://humanoid-getup.github.io/

METRA: Scalable Unsupervised RL with Metric-Aware Abstraction

Unsupervised pre-training strategies have proven to be highly effective in natural language processing and computer vision. Likewise, unsupervised reinforcement learning (RL) holds the promise of discovering a variety of potentially useful behaviors that can accelerate the learning of a wide array of downstream tasks. Previous unsupervised RL approaches have mainly focused on pure exploration and mutual information skill learning. However, despite the previous attempts, making unsupervised RL truly scalable still remains a major open challenge: pure exploration approaches might struggle in complex environments with large state spaces, where covering every possible transition is infeasible, and mutual information skill learning approaches might completely fail to explore the environment due to the lack of incentives. To make unsupervised RL scalable to complex, high-dimensional environments, we propose a novel unsupervised RL objective, which we call Metric-Aware Abstraction (METRA). Our main idea is, instead of directly covering the entire state space, to only cover a compact latent space Z that is metrically connected to the state space S by temporal distances. By learning to move in every direction in the latent space, METRA obtains a tractable set of diverse behaviors that approximately cover the state space, being scalable to high-dimensional environments. Through our experiments in five locomotion and manipulation environments, we demonstrate that METRA can discover a variety of useful behaviors even in complex, pixel-based environments, being the first unsupervised RL method that discovers diverse locomotion behaviors in pixel-based Quadruped and Humanoid. Our code and videos are available at https://seohong.me/projects/metra/

Universal Humanoid Motion Representations for Physics-Based Control

We present a universal motion representation that encompasses a comprehensive range of motor skills for physics-based humanoid control. Due to the high-dimensionality of humanoid control as well as the inherent difficulties in reinforcement learning, prior methods have focused on learning skill embeddings for a narrow range of movement styles (e.g. locomotion, game characters) from specialized motion datasets. This limited scope hampers its applicability in complex tasks. Our work closes this gap, significantly increasing the coverage of motion representation space. To achieve this, we first learn a motion imitator that can imitate all of human motion from a large, unstructured motion dataset. We then create our motion representation by distilling skills directly from the imitator. This is achieved using an encoder-decoder structure with a variational information bottleneck. Additionally, we jointly learn a prior conditioned on proprioception (humanoid's own pose and velocities) to improve model expressiveness and sampling efficiency for downstream tasks. Sampling from the prior, we can generate long, stable, and diverse human motions. Using this latent space for hierarchical RL, we show that our policies solve tasks using natural and realistic human behavior. We demonstrate the effectiveness of our motion representation by solving generative tasks (e.g. strike, terrain traversal) and motion tracking using VR controllers.

SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environments

While significant research progress has been made in robot learning for control, unique challenges arise when simultaneously co-optimizing morphology. Existing work has typically been tailored for particular environments or representations. In order to more fully understand inherent design and performance tradeoffs and accelerate the development of new breeds of soft robots, a comprehensive virtual platform with well-established tasks, environments, and evaluation metrics is needed. In this work, we introduce SoftZoo, a soft robot co-design platform for locomotion in diverse environments. SoftZoo supports an extensive, naturally-inspired material set, including the ability to simulate environments such as flat ground, desert, wetland, clay, ice, snow, shallow water, and ocean. Further, it provides a variety of tasks relevant for soft robotics, including fast locomotion, agile turning, and path following, as well as differentiable design representations for morphology and control. Combined, these elements form a feature-rich platform for analysis and development of soft robot co-design algorithms. We benchmark prevalent representations and co-design algorithms, and shed light on 1) the interplay between environment, morphology, and behavior; 2) the importance of design space representations; 3) the ambiguity in muscle formation and controller synthesis; and 4) the value of differentiable physics. We envision that SoftZoo will serve as a standard platform and template an approach toward the development of novel representations and algorithms for co-designing soft robots' behavioral and morphological intelligence.

Hybrid Systems Neural Control with Region-of-Attraction Planner

Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special treatments are required at mode switchings to stabilize the system. In this work, we propose a hierarchical, neural network (NN)-based method to control general hybrid systems. For each system mode, we first learn an NN Lyapunov function and an NN controller to ensure the states within the region of attraction (RoA) can be stabilized. Then an RoA NN estimator is learned across different modes. Upon mode switching, we propose a differentiable planner to ensure the states after switching can land in next mode's RoA, hence stabilizing the hybrid system. We provide novel theoretical stability guarantees and conduct experiments in car tracking control, pogobot navigation, and bipedal walker locomotion. Our method only requires 0.25X of the training time as needed by other learning-based methods. With low running time (10-50X faster than model predictive control (MPC)), our controller achieves a higher stability/success rate over other baselines such as MPC, reinforcement learning (RL), common Lyapunov methods (CLF), linear quadratic regulator (LQR), quadratic programming (QP) and Hamilton-Jacobian-based methods (HJB). The project page is on https://mit-realm.github.io/hybrid-clf.

ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills

Humanoid robots hold the potential for unparalleled versatility in performing human-like, whole-body skills. However, achieving agile and coordinated whole-body motions remains a significant challenge due to the dynamics mismatch between simulation and the real world. Existing approaches, such as system identification (SysID) and domain randomization (DR) methods, often rely on labor-intensive parameter tuning or result in overly conservative policies that sacrifice agility. In this paper, we present ASAP (Aligning Simulation and Real-World Physics), a two-stage framework designed to tackle the dynamics mismatch and enable agile humanoid whole-body skills. In the first stage, we pre-train motion tracking policies in simulation using retargeted human motion data. In the second stage, we deploy the policies in the real world and collect real-world data to train a delta (residual) action model that compensates for the dynamics mismatch. Then, ASAP fine-tunes pre-trained policies with the delta action model integrated into the simulator to align effectively with real-world dynamics. We evaluate ASAP across three transfer scenarios: IsaacGym to IsaacSim, IsaacGym to Genesis, and IsaacGym to the real-world Unitree G1 humanoid robot. Our approach significantly improves agility and whole-body coordination across various dynamic motions, reducing tracking error compared to SysID, DR, and delta dynamics learning baselines. ASAP enables highly agile motions that were previously difficult to achieve, demonstrating the potential of delta action learning in bridging simulation and real-world dynamics. These results suggest a promising sim-to-real direction for developing more expressive and agile humanoids.

WildLMa: Long Horizon Loco-Manipulation in the Wild

`In-the-wild' mobile manipulation aims to deploy robots in diverse real-world environments, which requires the robot to (1) have skills that generalize across object configurations; (2) be capable of long-horizon task execution in diverse environments; and (3) perform complex manipulation beyond pick-and-place. Quadruped robots with manipulators hold promise for extending the workspace and enabling robust locomotion, but existing results do not investigate such a capability. This paper proposes WildLMa with three components to address these issues: (1) adaptation of learned low-level controller for VR-enabled whole-body teleoperation and traversability; (2) WildLMa-Skill -- a library of generalizable visuomotor skills acquired via imitation learning or heuristics and (3) WildLMa-Planner -- an interface of learned skills that allow LLM planners to coordinate skills for long-horizon tasks. We demonstrate the importance of high-quality training data by achieving higher grasping success rate over existing RL baselines using only tens of demonstrations. WildLMa exploits CLIP for language-conditioned imitation learning that empirically generalizes to objects unseen in training demonstrations. Besides extensive quantitative evaluation, we qualitatively demonstrate practical robot applications, such as cleaning up trash in university hallways or outdoor terrains, operating articulated objects, and rearranging items on a bookshelf.

CrossLoco: Human Motion Driven Control of Legged Robots via Guided Unsupervised Reinforcement Learning

Human motion driven control (HMDC) is an effective approach for generating natural and compelling robot motions while preserving high-level semantics. However, establishing the correspondence between humans and robots with different body structures is not straightforward due to the mismatches in kinematics and dynamics properties, which causes intrinsic ambiguity to the problem. Many previous algorithms approach this motion retargeting problem with unsupervised learning, which requires the prerequisite skill sets. However, it will be extremely costly to learn all the skills without understanding the given human motions, particularly for high-dimensional robots. In this work, we introduce CrossLoco, a guided unsupervised reinforcement learning framework that simultaneously learns robot skills and their correspondence to human motions. Our key innovation is to introduce a cycle-consistency-based reward term designed to maximize the mutual information between human motions and robot states. We demonstrate that the proposed framework can generate compelling robot motions by translating diverse human motions, such as running, hopping, and dancing. We quantitatively compare our CrossLoco against the manually engineered and unsupervised baseline algorithms along with the ablated versions of our framework and demonstrate that our method translates human motions with better accuracy, diversity, and user preference. We also showcase its utility in other applications, such as synthesizing robot movements from language input and enabling interactive robot control.

Neural Circuit Architectural Priors for Embodied Control

Artificial neural networks for motor control usually adopt generic architectures like fully connected MLPs. While general, these tabula rasa architectures rely on large amounts of experience to learn, are not easily transferable to new bodies, and have internal dynamics that are difficult to interpret. In nature, animals are born with highly structured connectivity in their nervous systems shaped by evolution; this innate circuitry acts synergistically with learning mechanisms to provide inductive biases that enable most animals to function well soon after birth and learn efficiently. Convolutional networks inspired by visual circuitry have encoded useful biases for vision. However, it is unknown the extent to which ANN architectures inspired by neural circuitry can yield useful biases for other AI domains. In this work, we ask what advantages biologically inspired ANN architecture can provide in the domain of motor control. Specifically, we translate C. elegans locomotion circuits into an ANN model controlling a simulated Swimmer agent. On a locomotion task, our architecture achieves good initial performance and asymptotic performance comparable with MLPs, while dramatically improving data efficiency and requiring orders of magnitude fewer parameters. Our architecture is interpretable and transfers to new body designs. An ablation analysis shows that constrained excitation/inhibition is crucial for learning, while weight initialization contributes to good initial performance. Our work demonstrates several advantages of biologically inspired ANN architecture and encourages future work in more complex embodied control.

DyGait: Exploiting Dynamic Representations for High-performance Gait Recognition

Gait recognition is a biometric technology that recognizes the identity of humans through their walking patterns. Compared with other biometric technologies, gait recognition is more difficult to disguise and can be applied to the condition of long-distance without the cooperation of subjects. Thus, it has unique potential and wide application for crime prevention and social security. At present, most gait recognition methods directly extract features from the video frames to establish representations. However, these architectures learn representations from different features equally but do not pay enough attention to dynamic features, which refers to a representation of dynamic parts of silhouettes over time (e.g. legs). Since dynamic parts of the human body are more informative than other parts (e.g. bags) during walking, in this paper, we propose a novel and high-performance framework named DyGait. This is the first framework on gait recognition that is designed to focus on the extraction of dynamic features. Specifically, to take full advantage of the dynamic information, we propose a Dynamic Augmentation Module (DAM), which can automatically establish spatial-temporal feature representations of the dynamic parts of the human body. The experimental results show that our DyGait network outperforms other state-of-the-art gait recognition methods. It achieves an average Rank-1 accuracy of 71.4% on the GREW dataset, 66.3% on the Gait3D dataset, 98.4% on the CASIA-B dataset and 98.3% on the OU-MVLP dataset.

UBSoft: A Simulation Platform for Robotic Skill Learning in Unbounded Soft Environments

It is desired to equip robots with the capability of interacting with various soft materials as they are ubiquitous in the real world. While physics simulations are one of the predominant methods for data collection and robot training, simulating soft materials presents considerable challenges. Specifically, it is significantly more costly than simulating rigid objects in terms of simulation speed and storage requirements. These limitations typically restrict the scope of studies on soft materials to small and bounded areas, thereby hindering the learning of skills in broader spaces. To address this issue, we introduce UBSoft, a new simulation platform designed to support unbounded soft environments for robot skill acquisition. Our platform utilizes spatially adaptive resolution scales, where simulation resolution dynamically adjusts based on proximity to active robotic agents. Our framework markedly reduces the demand for extensive storage space and computation costs required for large-scale scenarios involving soft materials. We also establish a set of benchmark tasks in our platform, including both locomotion and manipulation tasks, and conduct experiments to evaluate the efficacy of various reinforcement learning algorithms and trajectory optimization techniques, both gradient-based and sampling-based. Preliminary results indicate that sampling-based trajectory optimization generally achieves better results for obtaining one trajectory to solve the task. Additionally, we conduct experiments in real-world environments to demonstrate that advancements made in our UBSoft simulator could translate to improved robot interactions with large-scale soft material. More videos can be found at https://vis-www.cs.umass.edu/ubsoft/.

Text2Reward: Automated Dense Reward Function Generation for Reinforcement Learning

Designing reward functions is a longstanding challenge in reinforcement learning (RL); it requires specialized knowledge or domain data, leading to high costs for development. To address this, we introduce Text2Reward, a data-free framework that automates the generation of dense reward functions based on large language models (LLMs). Given a goal described in natural language, Text2Reward generates dense reward functions as an executable program grounded in a compact representation of the environment. Unlike inverse RL and recent work that uses LLMs to write sparse reward codes, Text2Reward produces interpretable, free-form dense reward codes that cover a wide range of tasks, utilize existing packages, and allow iterative refinement with human feedback. We evaluate Text2Reward on two robotic manipulation benchmarks (ManiSkill2, MetaWorld) and two locomotion environments of MuJoCo. On 13 of the 17 manipulation tasks, policies trained with generated reward codes achieve similar or better task success rates and convergence speed than expert-written reward codes. For locomotion tasks, our method learns six novel locomotion behaviors with a success rate exceeding 94%. Furthermore, we show that the policies trained in the simulator with our method can be deployed in the real world. Finally, Text2Reward further improves the policies by refining their reward functions with human feedback. Video results are available at https://text-to-reward.github.io

MoCapAct: A Multi-Task Dataset for Simulated Humanoid Control

Simulated humanoids are an appealing research domain due to their physical capabilities. Nonetheless, they are also challenging to control, as a policy must drive an unstable, discontinuous, and high-dimensional physical system. One widely studied approach is to utilize motion capture (MoCap) data to teach the humanoid agent low-level skills (e.g., standing, walking, and running) that can then be re-used to synthesize high-level behaviors. However, even with MoCap data, controlling simulated humanoids remains very hard, as MoCap data offers only kinematic information. Finding physical control inputs to realize the demonstrated motions requires computationally intensive methods like reinforcement learning. Thus, despite the publicly available MoCap data, its utility has been limited to institutions with large-scale compute. In this work, we dramatically lower the barrier for productive research on this topic by training and releasing high-quality agents that can track over three hours of MoCap data for a simulated humanoid in the dm_control physics-based environment. We release MoCapAct (Motion Capture with Actions), a dataset of these expert agents and their rollouts, which contain proprioceptive observations and actions. We demonstrate the utility of MoCapAct by using it to train a single hierarchical policy capable of tracking the entire MoCap dataset within dm_control and show the learned low-level component can be re-used to efficiently learn downstream high-level tasks. Finally, we use MoCapAct to train an autoregressive GPT model and show that it can control a simulated humanoid to perform natural motion completion given a motion prompt. Videos of the results and links to the code and dataset are available at https://microsoft.github.io/MoCapAct.

MyoDex: A Generalizable Prior for Dexterous Manipulation

Human dexterity is a hallmark of motor control. Our hands can rapidly synthesize new behaviors despite the complexity (multi-articular and multi-joints, with 23 joints controlled by more than 40 muscles) of musculoskeletal sensory-motor circuits. In this work, we take inspiration from how human dexterity builds on a diversity of prior experiences, instead of being acquired through a single task. Motivated by this observation, we set out to develop agents that can build upon their previous experience to quickly acquire new (previously unattainable) behaviors. Specifically, our approach leverages multi-task learning to implicitly capture task-agnostic behavioral priors (MyoDex) for human-like dexterity, using a physiologically realistic human hand model - MyoHand. We demonstrate MyoDex's effectiveness in few-shot generalization as well as positive transfer to a large repertoire of unseen dexterous manipulation tasks. Agents leveraging MyoDex can solve approximately 3x more tasks, and 4x faster in comparison to a distillation baseline. While prior work has synthesized single musculoskeletal control behaviors, MyoDex is the first generalizable manipulation prior that catalyzes the learning of dexterous physiological control across a large variety of contact-rich behaviors. We also demonstrate the effectiveness of our paradigms beyond musculoskeletal control towards the acquisition of dexterity in 24 DoF Adroit Hand. Website: https://sites.google.com/view/myodex

QUAR-VLA: Vision-Language-Action Model for Quadruped Robots

The important manifestation of robot intelligence is the ability to naturally interact and autonomously make decisions. Traditional approaches to robot control often compartmentalize perception, planning, and decision-making, simplifying system design but limiting the synergy between different information streams. This compartmentalization poses challenges in achieving seamless autonomous reasoning, decision-making, and action execution. To address these limitations, a novel paradigm, named Vision-Language-Action tasks for QUAdruped Robots (QUAR-VLA), has been introduced in this paper. This approach tightly integrates visual information and instructions to generate executable actions, effectively merging perception, planning, and decision-making. The central idea is to elevate the overall intelligence of the robot. Within this framework, a notable challenge lies in aligning fine-grained instructions with visual perception information. This emphasizes the complexity involved in ensuring that the robot accurately interprets and acts upon detailed instructions in harmony with its visual observations. Consequently, we propose QUAdruped Robotic Transformer (QUART), a family of VLA models to integrate visual information and instructions from diverse modalities as input and generates executable actions for real-world robots and present QUAdruped Robot Dataset (QUARD), a large-scale multi-task dataset including navigation, complex terrain locomotion, and whole-body manipulation tasks for training QUART models. Our extensive evaluation (4000 evaluation trials) shows that our approach leads to performant robotic policies and enables QUART to obtain a range of emergent capabilities.

Subequivariant Graph Reinforcement Learning in 3D Environments

Learning a shared policy that guides the locomotion of different agents is of core interest in Reinforcement Learning (RL), which leads to the study of morphology-agnostic RL. However, existing benchmarks are highly restrictive in the choice of starting point and target point, constraining the movement of the agents within 2D space. In this work, we propose a novel setup for morphology-agnostic RL, dubbed Subequivariant Graph RL in 3D environments (3D-SGRL). Specifically, we first introduce a new set of more practical yet challenging benchmarks in 3D space that allows the agent to have full Degree-of-Freedoms to explore in arbitrary directions starting from arbitrary configurations. Moreover, to optimize the policy over the enlarged state-action space, we propose to inject geometric symmetry, i.e., subequivariance, into the modeling of the policy and Q-function such that the policy can generalize to all directions, improving exploration efficiency. This goal is achieved by a novel SubEquivariant Transformer (SET) that permits expressive message exchange. Finally, we evaluate the proposed method on the proposed benchmarks, where our method consistently and significantly outperforms existing approaches on single-task, multi-task, and zero-shot generalization scenarios. Extensive ablations are also conducted to verify our design. Code and videos are available on our project page: https://alpc91.github.io/SGRL/.