Action Spaces for Robot Learning

An action space is the interface between a policy and the rest of the robot: what the network predicts, which errors the controller absorbs, how often inference runs and whether embodiments share labels. In Open X-Embodiment, the same seven numbers can mean absolute or relative positions or velocities^{Source 10}10 Open X-Embodiment Collaboration et al. 2023, Open X-Embodiment: Robotic Learning Datasets and RT-X Models. Open X-Embodiment Collaboration, Abby O'Neill, Abdul Rehman et al., 2023.

Paper figure: Yuchun Feng et al. / arXiv. Licence: CC BY 4.0.

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The contract has four parts

A contract names coordinates (joint, Cartesian, object-relative or another frame), semantics (absolute target, delta, velocity, force, torque or controller parameter), timing (rate, horizon and stale-prediction handling) and execution (interpolation, clipping, inverse kinematics, feedback and safety limits). DROID records equivalent commands in several action spaces^{Source 11}11 Khazatsky et al. 2024, DROID: A Large-Scale In-The-Wild Robot Manipulation Dataset. Alexander Khazatsky, Karl Pertsch, Suraj Nair, 2024, and robosuite's controllers span joint and Cartesian spaces^{Source 12}12 Zhu et al. 2020, robosuite: A Modular Simulation Framework and Benchmark for Robot Learning. Yuke Zhu, Josiah Wong, Ajay Mandlekar et al., 2020.

Joint-space actions

Joint position targets are a common imitation baseline; ACT predicts chunks of absolute joint-and-gripper targets for two ViperX arms^{Source 2}2 Zhao et al. 2023, Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware. Tony Z. Zhao, Vikash Kumar, Sergey Levine et al., RSS 2023. The controller interpolates and enforces limits, but one shoulder angle moves different arms differently.

Joint velocity targets drift when integrated; the kinematics module derives the forward map and Jacobian both need^{Source 1}1 Lynch et al. 2017, Modern Robotics: Mechanics, Planning, and Control. Kevin M. Lynch, Frank C. Park, Cambridge University Press, 2017. In locomotion RL, target joint angles with local feedback beat raw torques for learning speed, robustness and motion quality^{Source 13}13 Peng et al. 2016, Learning Locomotion Skills Using DeepRL: Does the Choice of Action Space Matter?. Xue Bin Peng, Michiel van de Panne, arXiv preprint (SCA 2017), 2016.

Cartesian actions

Cartesian actions say what the tool should do. Once range and frame are fixed, relative deltas from the current pose label arms with different joint counts and link lengths alike, provided each robot supplies inverse kinematics or an operational-space controller; Khatib's 1987 operational space formulation unifies motion and force control^{Source 7}7 Khatib 1987, A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation. Oussama Khatib, IEEE J. Robotics and Automation, 1987. Euler angles and quaternions are discontinuous as network outputs, while 6D representations are continuous^{Source 14}14 Zhou et al. 2018, On the Continuity of Rotation Representations in Neural Networks. Yi Zhou, Connelly Barnes, Jingwan Lu et al., 2018.

GR00T N1.6's notes find relative actions smoother and more accurate than absolute ones but prone to error accumulation on small datasets^{Source 15}15 GEAR Team et al. 2025, GR00T N1.6: An Improved Open Foundation Model for Generalist Humanoid Robots. GEAR Team, Allison Azzolini, Johan Bjorck et al., 2025, and in matched VLA pretraining ablations a unified end-effector-relative representation was critical for cross-embodiment transfer^{Source 16}16 Wang et al. 2026, Rethinking Visual-Language-Action Model Scaling: Alignment, Mixture, and Regularization. Ye Wang, Sipeng Zheng, Hao Luo et al., 2026. X-VLA instead learns a separate set of soft-prompt embeddings for each data source as embodiment-specific prompts^{Source 27}27 Zheng et al. 2025, X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Model. Jinliang Zheng, Jianxiong Li, Zhihao Wang et al., 2025.

Torque and impedance actions

Torque actions expose dynamics and contact; Levine et al. mapped raw images to motor torques^{Source 17}17 Levine et al. 2015, End-to-End Training of Deep Visuomotor Policies. Sergey Levine, Chelsea Finn, Trevor Darrell et al., 2015. They need a high rate and a safety layer that holds when the output is wrong: libfranka sends 1 kHz commands in five modes, including gravity- and friction-compensated joint torque^{Source 9}9 Franka Robotics 2026, Franka Control Interface Documentation. Franka Robotics, Franka Robotics, as of 2026-08-20, while Rudin et al.'s locomotion pipeline sends joint-position targets to a PD controller^{Source 18}18 Rudin et al. 2021, Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning. Nikita Rudin, David Hoeller, Philipp Reist et al., CoRL 2021.

Paper figure: Yifan Hou et al. / arXiv. Licence: CC BY 4.0.

Impedance actions sit between: the policy picks a pose target plus stiffness and damping, and a controller turns error into force. Hogan judged position or force control alone inadequate for manipulation^{Source 19}19 Hogan 1985, Impedance Control: An Approach to Manipulation: Part I—Theory. Neville Hogan, ASME J. Dynamic Systems, Measurement, and Control, 1985. Task-space impedance references needed the fewest samples against torque, joint PD and inverse dynamics^{Source 20}20 Varin et al. 2019, A Comparison of Action Spaces for Learning Manipulation Tasks. Patrick Varin, Lev Grossman, Scott Kuindersma, 2019, and Adaptive Compliance Policy's predicted compliance beats position-only visuomotor policies by over 50%^{Source 21}21 Hou et al. 2024, Adaptive Compliance Policy: Learning Approximate Compliance for Diffusion Guided Control. Yifan Hou, Zeyi Liu, Cheng Chi et al., arXiv preprint (ICRA 2025), 2024.

Chunks change the time axis

An action chunkaction chunkingAction chunking is predicting a sequence of future actions in one inference instead of a single action per timestep. Introduced with ACT on ALOHA, it divides an episode's sequential decisions by the chunk length, reducing compounding error and giving the policy temporal context to represent pauses. The cost is commitment to a plan between replans. predicts several steps per inference, which helped ACT and two retrofitted baselines (action chunking)^{Source 2}2 Zhao et al. 2023, Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware. Tony Z. Zhao, Vikash Kumar, Sergey Levine et al., RSS 2023; Diffusion Policy executes the first part of a predicted horizon, then replans^{Source 3}3 Chi et al. 2023, Diffusion Policy: Visuomotor Policy Learning via Action Diffusion. Cheng Chi, Zhenjia Xu, Siyuan Feng et al., 2023. Open-loop chunks go stale when contact changes the scene, which receding horizons, temporal ensembling and real-time chunk replacement each address^{Source 4}4 Black et al. 2025, Real-Time Execution of Action Chunking Flow Policies. Kevin Black, Manuel Y. Galliker, Sergey Levine, 2025 (real-time execution).

Rates differ by layer: GEN-1.5 produces 100 Hz action trajectories^{Source 28}28 Generalist Team 2026, GEN-1.5: Embodied Foundation Models are One-Shot Learners. Generalist Team, Generalist AI blog, 2026, and Helix 02's S0 sends joint-level actuator commands at 1 kHz beneath S1's 200 Hz joint targets^{Source 29}29 Figure AI 2026, Introducing Helix 02: Full-Body Autonomy. Figure AI, 2026. Report predicted and executed horizons separately.

Tokens change the output geometry

RT-2^{Source 5}5 Brohan et al. 2023, RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control. Anthony Brohan, Noah Brown, Justice Carbajal et al., 2023 and OpenVLA map continuous actions to vocabulary tokens to reuse language-model training, OpenVLA binning seven dimensions into 256 values^{Source 6}6 Kim et al. 2024, OpenVLA: An Open-Source Vision-Language-Action Model. Moo Jin Kim, Karl Pertsch, Siddharth Karamcheti et al., 2024. Binning allows cross-entropy but limits resolution and adds autoregressive decoding to latency. FAST compresses a chunk's frequency coefficients with byte-pair encoding, far better than per-dimension binning, and its universal FAST+ tokenizer was trained on 1M real robot action trajectories^{Source 8}8 Pertsch et al. 2025, FAST: Efficient Action Tokenization for Vision-Language-Action Models. Karl Pertsch, Kyle Stachowicz, Brian Ichter et al., 2025. VQ-BeT's vector-quantized actions infer 5 times faster than Diffusion Policy^{Source 22}22 Lee et al. 2024, Behavior Generation with Latent Actions. Seungjae Lee, Yibin Wang, Haritheja Etukuru et al., 2024, and LAP writes end-effector motions as short natural-language phrases, with LAP-3B averaging over 50% zero-shot success on three unseen robots^{Source 30}30 Zha et al. 2026, LAP: Language-Action Pre-Training Enables Zero-shot Cross-Embodiment Transfer. Lihan Zha, Asher J. Hancock, Mingtong Zhang et al., 2026.

Continuous heads skip tokens: OpenVLA-OFT's continuous actions, parallel decoding and L1 objective lifted LIBERO success from 76.5% to 97.1%^{Source 23}23 Kim et al. 2025, Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success. Moo Jin Kim, Chelsea Finn, Percy Liang, 2025, and Figure says Helix outputs continuous control to avoid tokenization^{Source 24}24 Figure AI 2025, Helix: A Vision-Language-Action Model for Generalist Humanoid Control. Figure AI, 2025. Naively adding a continuous expert to a VLM harms training speed and knowledge transfer, which knowledge insulation addresses^{Source 25}25 Driess et al. 2025, Knowledge Insulating Vision-Language-Action Models: Train Fast, Run Fast, Generalize Better. Danny Driess, Jost Tobias Springenberg, Brian Ichter et al., 2025.

Zeji Yi, Max Simchowitz, Guanya Shi and colleagues at Carnegie Mellon and Amazon FAR (October 2026) gave one PaliGemma VLA four action heads: continuous or binned into 512 values, each predicted in one pass or by iterative flow. On simulated RoboCasa, over five seeds of 500 episodes, binned flow reached 53.9% success, continuous flow 52.7% and one-pass continuous regression 38.8%. One-pass binned prediction reached 27.1%, which the authors trace to tokens chosen independently across time steps and action dimensions; guidance raised it to 49.2%^{Source 31}31 Yi et al. 2026, When Do Discrete Actions Make Good Continuous Controllers?. Zeji Yi, Soham Dasgupta, Xinyang Zhang et al., 2026.

A selection rule

Choose the lowest-level action the task requires and the platform supports safely. Across 13,000+ real rollouts and 500+ models, predicting delta actions consistently helped, with joint space favoring control stability and task space favoring generalization^{Source 26}26 Feng et al. 2026, Demystifying Action Space Design for Robotic Manipulation Policies. Yuchun Feng, Jinliang Zheng, Zhihao Wang et al., 2026. Hold controller, rate, horizon and observation history fixed when comparing architectures, or the comparison measures interface changes.