mlsanityData to 14 Oct 2026

Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion

arXiv 2308.12517 ↗First posted 24 Aug 2023cs.RO cs.AI cs.LGcited by 47

Not on the map. Why?

Cited by 27 in Deep reinforcement learning methods, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Several earlier studies have shown impressive control performance in complex robotic systems by designing the controller using a neural network and training it with model-free reinforcement learning. However, these outstanding controllers with natural motion style and high task performance are developed through extensive reward engineering, which is a highly laborious and time-consuming process of designing numerous reward terms and determining suitable reward coefficients. In this work, we propose a novel reinforcement learning framework for training neural network controllers for complex robotic systems consisting of both rewards and constraints. To let the engineers appropriately reflect their intent to constraints and handle them with minimal computation overhead, two constraint types and an efficient policy optimization algorithm are suggested. The learning framework is applied to train locomotion controllers for several legged robots with different morphology and physical attributes to traverse challenging terrains. Extensive simulation and real-world experiments demonstrate that performant controllers can be trained with significantly less reward engineering, by tuning only a single reward coefficient. Furthermore, a more straightforward and intuitive engineering process can be utilized, thanks to the interpretability and generalizability of constraints. The summary video is available at https://youtu.be/KAlm3yskhvM.

Key facts. Cited by 47 papers in the map (data through 14 Oct 2026). Builds on 48 of its 74 references that are in the map. First posted on arXiv 24 Aug 2023.

Builds on

48 of 74 references.

References · 48

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2017Proximal Policy Optimization Algorithmscited by 15,215
  3. 2015Trust Region Policy Optimizationcited by 2,580
  4. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,367
  5. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 2,026
  6. 2016Generative Adversarial Imitation Learningcited by 1,597
  7. 2023Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardwarecited by 1,568
  8. 2017Constrained Policy Optimizationcited by 983
  9. 2018Learning Dexterous In-Hand Manipulationcited by 687
  10. 2017Sim-to-Real Transfer of Robotic Control with Dynamics Randomizationcited by 672
  11. 2020Learning Quadrupedal Locomotion over Challenging Terraincited by 604
  12. 2021Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learningcited by 512
36 more
  1. 2021RMA: Rapid Motor Adaptation for Legged Robotscited by 508
  2. 2019Learning agile and dynamic motor skills for legged robotscited by 504
  3. 2018Reward Constrained Policy Optimizationcited by 417
  4. 2022Learning robust perceptive locomotion for quadrupedal robots in the wildcited by 382
  5. 2016Deep Reinforcement Learning for Robotic Manipulation with Asynchronous Off-Policy Updatescited by 353
  6. 2015Risk-Constrained Reinforcement Learning with Percentile Risk Criteriacited by 337
  7. 2019Deep Dynamics Models for Learning Dexterous Manipulationcited by 206
  8. 2020Projection-Based Constrained Policy Optimizationcited by 203
  9. 2023Real-World Humanoid Locomotion with Reinforcement Learningcited by 187
  10. 2022Rapid Locomotion via Reinforcement Learningcited by 168
  11. 2017Emergence of Locomotion Behaviours in Rich Environmentscited by 165
  12. 2023ANYmal Parkour: Learning Agile Navigation for Quadrupedal Robotscited by 152
  13. 2022Legged Locomotion in Challenging Terrains using Egocentric Visioncited by 151
  14. 2020CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guaranteecited by 134
  15. 2019IPO: Interior-point Policy Optimization under Constraintscited by 132
  16. 2022Deep Whole-Body Control: Learning a Unified Policy for Manipulation and Locomotioncited by 121
  17. 2020Conservative Safety Critics for Explorationcited by 113
  18. 2020BADGR: An Autonomous Self-Supervised Learning-Based Navigation Systemcited by 102
  19. 2017Virtual-to-real Deep Reinforcement Learning: Continuous Control of Mobile Robots for Mapless Navigationcited by 98
  20. 2017Control of a Quadrotor with Reinforcement Learningcited by 92
  21. 2022Adversarial Motion Priors Make Good Substitutes for Complex Reward Functionscited by 89
  22. 2022Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotioncited by 88
  23. 2022Penalized Proximal Policy Optimization for Safe Reinforcement Learningcited by 68
  24. 2018Learning Symmetric and Low-energy Locomotioncited by 61
  25. 2020ALLSTEPS: Curriculum-driven Learning of Stepping Stone Skillscited by 54
  26. 2022GenLoco: Generalized Locomotion Controllers for Quadrupedal Robotscited by 48
  27. 2018Feedback Control For Cassie With Deep Reinforcement Learningcited by 45
  28. 2023Legs as Manipulator: Pushing Quadrupedal Agility Beyond Locomotioncited by 39
  29. 2022Perceptive Locomotion through Nonlinear Model Predictive Controlcited by 38
  30. 2022Safe Reinforcement Learning for Legged Locomotioncited by 35
  31. 2022OPT-Mimic: Imitation of Optimized Trajectories for Dynamic Quadruped Behaviorscited by 35
  32. 2022Learning Free Gait Transition for Quadruped Robots via Phase-Guided Controllercited by 29
  33. 2020Guided Constrained Policy Optimization for Dynamic Quadrupedal Robot Locomotioncited by 25
  34. 2022TAMOLS: Terrain-Aware Motion Optimization for Legged Systemscited by 14
  35. 2022Learning Forward Dynamics Model and Informed Trajectory Sampler for Safe Quadruped Navigationcited by 6
  36. 2021Learning multiple gaits of quadruped robot using hierarchical reinforcement learningcited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 16; 2025: 15; 2026: 14.

47 papers.

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  1. 2024DrEureka: Language Model Guided Sim-To-Real Transfercited by 83
  2. 2024One Policy to Run Them All: an End-to-end Learning Approach to Multi-Embodiment Locomotioncited by 43
  3. 2024CaT: Constraints as Terminations for Legged Locomotion Reinforcement Learningcited by 23
  4. 2025LocoFormer: Generalist Locomotion via Long-context Adaptationcited by 20
  5. 2024SoloParkour: Constrained Reinforcement Learning for Visual Locomotion from Privileged Experiencecited by 14
  6. 2024Stage-Wise Reward Shaping for Acrobatic Robots: A Constrained Multi-Objective Reinforcement Learning Approachcited by 13
  7. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 12
  8. 2024A Learning Framework for Diverse Legged Robot Locomotion Using Barrier-Based Style Rewardscited by 12
  9. 2026VLANeXt: Recipes for Building Strong VLA Modelscited by 12
  10. 2023Gradient Shaping for Multi-Constraint Safe Reinforcement Learningcited by 10
  11. 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environmentscited by 9
  12. 2024PA-LOCO: Learning Perturbation-Adaptive Locomotion for Quadruped Robotscited by 8
35 more
  1. 2025SPiDR: A Simple Approach for Zero-Shot Safety in Sim-to-Real Transfercited by 8
  2. 2023DecAP: Decaying Action Priors for Accelerated Imitation Learning of Torque-Based Legged Locomotion Policiescited by 7
  3. 2024Automatic Environment Shaping is the Next Frontier in RLcited by 7
  4. 2025RAPID: Robust and Agile Planner Using Inverse Reinforcement Learning for Vision-Based Drone Navigationcited by 6
  5. 2024Learning Semantic Traversability with Egocentric Video and Automated Annotation Strategycited by 5
  6. 2025TAR: Teacher-Aligned Representations via Contrastive Learning for Quadrupedal Locomotioncited by 5
  7. 2024Legged Robot State Estimation With Invariant Extended Kalman Filter Using Neural Measurement Networkcited by 4
  8. 2024AnyBipe: An End-to-End Framework for Training and Deploying Bipedal Robots Guided by Large Language Modelscited by 3
  9. 2025Spectral Normalization for Lipschitz-Constrained Policies on Learning Humanoid Locomotioncited by 3
  10. 2024Reinforcement Learning from Wild Animal Videoscited by 2
  11. 2025QuietPaw: Learning Quadrupedal Locomotion with Versatile Noise Preference Alignmentcited by 2
  12. 2026Toward Reliable Sim-to-Real Predictability for MoE-based Robust Quadrupedal Locomotioncited by 2
  13. 2024Learning Rapid Turning, Aerial Reorientation, and Balancing using Manipulator as a Tailcited by 1
  14. 2025BarlowWalk: Self-supervised Representation Learning for Legged Robot Terrain-adaptive Locomotioncited by 1
  15. 2025Constrained Reinforcement Learning for Unstable Point-Feet Bipedal Locomotion Applied to the Bolt Robotcited by 1
  16. 2025MASH: Cooperative-Heterogeneous Multi-Agent Reinforcement Learning for Single Humanoid Robot Locomotioncited by 1
  17. 2025Periodic Skill Discoverycited by 1
  18. 2026ECO: Energy-Constrained Optimization with Reinforcement Learning for Humanoid Walkingcited by 1
  19. 2026TRANS: Terrain-aware Reinforcement Learning for Agile Navigation of Quadruped Robots under Social Interactionscited by 1
  20. 2026MPC-Injection: Biasing Off-Policy Locomotion RL Toward Controller-Induced Behavior Basinscited by 1
  21. 2026Agile perceptive multi-skill locomotion for quadrupedal robots in the wildcited by 1
  22. 2024Adversarial Constrained Policy Optimization: Improving Constrained Reinforcement Learning by Adapting Budgetscited by 0
  23. 2025PALo: Learning Posture-Aware Locomotion for Quadruped Robotscited by 0
  24. 2025Rule-Based Conflict-Free Decision Framework in Swarm Confrontationcited by 0
  25. 2025GenTe: Generative Real-world Terrains for General Legged Robot Locomotion Controlcited by 0
  26. 2025Dynamic Legged Ball Manipulation on Rugged Terrains with Hierarchical Reinforcement Learningcited by 0
  27. 2025Whole-Body Constrained Learning for Legged Locomotion via Hierarchical Optimizationcited by 0
  28. 2026Beyond Safety Filtering: Control Barrier Function-Informed Reinforcement Learning for Connected and Automated Vehiclescited by 0
  29. 2026Robust Fall Recovery for Armless Bipedal-Wheeled Robots Via Force-Guided Learningcited by 0
  30. 2026LoComposition: Terrain-Adaptive Energy-Efficient Quadruped Locomotion without Gait Priorscited by 0
  31. 2026DynaWM: Dynamics-Aware Distillation with World Model and Momentum Targets for Smooth Locomotion over Continuous Stairscited by 0
  32. 2026PPO-EAL: Exact Augmented Lagrangian Proximal Policy Optimization for Safe Robotic Controlcited by 0
  33. 2026Navigating the Proximity-Safety Balance: Constraint Decomposition for Human Following in Pedestrian Crowdscited by 0
  34. 2026Smoothness as a Constraint for Stable Humanoid Locomotioncited by 0
  35. 2026Phase-Gated Constrained Reinforcement Learning for End-to-End Capture and Detumbling of Non-Cooperative Targetscited by 0