Learning Risk-Aware Quadrupedal Locomotion using Distributional Reinforcement Learning
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Abstract (arXiv)
Deployment in hazardous environments requires robots to understand the risks associated with their actions and movements to prevent accidents. Despite its importance, these risks are not explicitly modeled by currently deployed locomotion controllers for legged robots. In this work, we propose a risk sensitive locomotion training method employing distributional reinforcement learning to consider safety explicitly. Instead of relying on a value expectation, we estimate the complete value distribution to account for uncertainty in the robot's interaction with the environment. The value distribution is consumed by a risk metric to extract risk sensitive value estimates. These are integrated into Proximal Policy Optimization (PPO) to derive our method, Distributional Proximal Policy Optimization (DPPO). The risk preference, ranging from risk-averse to risk-seeking, can be controlled by a single parameter, which enables to adjust the robot's behavior dynamically. Importantly, our approach removes the need for additional reward function tuning to achieve risk sensitivity. We show emergent risk sensitive locomotion behavior in simulation and on the quadrupedal robot ANYmal. Videos of the experiments and code are available at https://sites.google.com/leggedrobotics.com/risk-aware-locomotion.
Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 40 of its 55 references that are in the map. First posted on arXiv 25 Sep 2023.
Builds on
40 of 55 references.
References · 40
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28 more
- 2022Learning robust perceptive locomotion for quadrupedal robots in the wildcited by 382
- 2018Implicit Quantile Networks for Distributional Reinforcement Learningcited by 369
- 2018Sim-to-Real: Learning Agile Locomotion For Quadruped Robotscited by 319
- 2018Distributed Distributional Deterministic Policy Gradientscited by 199
- 2020Controlling Overestimation Bias with Truncated Mixture of Continuous Distributional Quantile Criticscited by 165
- 2022Legged Locomotion in Challenging Terrains using Egocentric Visioncited by 151
- 2023Learning Agile Soccer Skills for a Bipedal Robot with Deep Reinforcement Learningcited by 133
- 2017The Cramer Distance as a Solution to Biased Wasserstein Gradientscited by 119
- 2019Fully Parameterized Quantile Function for Distributional Reinforcement Learningcited by 88
- 2021Legged Robots that Keep on Learning: Fine-Tuning Locomotion Policies in the Real Worldcited by 71
- 2021Risk-Averse Offline Reinforcement Learningcited by 65
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- 2022Elevation Mapping for Locomotion and Navigation using GPUcited by 43
- 2023An Analysis of Quantile Temporal-Difference Learningcited by 31
- 2019Quantile QT-Opt for Risk-Aware Vision-Based Robotic Graspingcited by 29
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- 2021GMAC: A Distributional Perspective on Actor-Critic Frameworkcited by 16
- 2020Sample-based Distributional Policy Gradientcited by 14
- 2022Team CERBERUS Wins the DARPA Subterranean Challenge: Technical Overview and Lessons Learnedcited by 14
- 2021Addressing Inherent Uncertainty: Risk-Sensitive Behavior Generation for Automated Driving using Distributional Reinforcement Learningcited by 13
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Citing papers per year: 2024: 4; 2025: 5; 2026: 5.
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- 2024Rethinking Robustness Assessment: Adversarial Attacks on Learning-based Quadrupedal Locomotion Controllerscited by 14
- 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environmentscited by 9
- 2024Preference Aligned Diffusion Planner for Quadrupedal Locomotion Controlcited by 7
- 2025Return Capping: Sample-Efficient CVaR Policy Gradient Optimisationcited by 6
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learningcited by 3
- 2024Myopically Verifiable Probabilistic Certificates for Safe Control and Learningcited by 1
- 2025Scoop-and-Toss: Dynamic Object Collection for Quadrupedal Systemscited by 0
- 2025Distributional Inverse Reinforcement Learningcited by 0
- 2025Risk-Aware Reinforcement Learning with Bandit-Based Adaptation for Quadrupedal Locomotioncited by 0
- 2026Moments Matter:Stabilizing Policy Optimization using Return Distributionscited by 0
- 2026Distributional Active Inferencecited by 0
- 2026Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinitycited by 0
2 more
- 2026Predictive Safety Curricula for Robust Legged Locomotion29 Sep 2026
- 2026Risk-Aware Reinforcement Learning for Mobile Manipulation4 Mar 2026
- 2026Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinity3 Feb 2026
- 2026Distributional Active Inference28 Jan 2026
- 2026Moments Matter:Stabilizing Policy Optimization using Return Distributions5 Jan 2026
- 2025Risk-Aware Reinforcement Learning with Bandit-Based Adaptation for Quadrupedal Locomotion16 Oct 2025
- 2025Distributional Inverse Reinforcement Learning3 Oct 2025
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learning27 Jul 2025
- 2025Scoop-and-Toss: Dynamic Object Collection for Quadrupedal Systems11 Jun 2025
- 2025Return Capping: Sample-Efficient CVaR Policy Gradient Optimisation29 Apr 2025
- 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments13 Dec 2024
- 2024Preference Aligned Diffusion Planner for Quadrupedal Locomotion Control17 Oct 2024
- 2024Rethinking Robustness Assessment: Adversarial Attacks on Learning-based Quadrupedal Locomotion Controllerscited by 14
- 2025Return Capping: Sample-Efficient CVaR Policy Gradient Optimisationcited by 6
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learningcited by 3
- 2025Risk-Aware Reinforcement Learning with Bandit-Based Adaptation for Quadrupedal Locomotioncited by 0
- 2026Moments Matter:Stabilizing Policy Optimization using Return Distributionscited by 0
- 2026Distributional Active Inferencecited by 0
- 2026Risk-Aware Reinforcement Learning for Mobile Manipulationcited by 0
- 2026Risk-Aware Reinforcement Learning for Mobile Manipulation4 Mar 2026
- 2026Distributional Active Inference28 Jan 2026
- 2026Moments Matter:Stabilizing Policy Optimization using Return Distributions5 Jan 2026
- 2025Risk-Aware Reinforcement Learning with Bandit-Based Adaptation for Quadrupedal Locomotion16 Oct 2025
- 2025Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learning27 Jul 2025
- 2025Return Capping: Sample-Efficient CVaR Policy Gradient Optimisation29 Apr 2025
- 2024Rethinking Robustness Assessment: Adversarial Attacks on Learning-based Quadrupedal Locomotion Controllers21 May 2024
- 2025Distributional Inverse Reinforcement Learningcited by 0
- 2025Distributional Inverse Reinforcement Learning3 Oct 2025
- 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environmentscited by 9
- 2024Myopically Verifiable Probabilistic Certificates for Safe Control and Learningcited by 1
- 2025Scoop-and-Toss: Dynamic Object Collection for Quadrupedal Systemscited by 0
- 2026Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinitycited by 0
- 2026Predictive Safety Curricula for Robust Legged Locomotioncited by 0
- 2026Predictive Safety Curricula for Robust Legged Locomotion29 Sep 2026
- 2026Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinity3 Feb 2026
- 2025Scoop-and-Toss: Dynamic Object Collection for Quadrupedal Systems11 Jun 2025
- 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments13 Dec 2024
- 2024Myopically Verifiable Probabilistic Certificates for Safe Control and Learning23 Apr 2024
Similar, not cited
Close in wording, no citation either way
- 2026Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering
- 2025Sampling Strategies for Robust Universal Quadrupedal Locomotion Policies
- 2026Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields
- 2025Learning Robotic Policy with Imagined Transition: Mitigating the Trade-off between Robustness and Optimality
- 2023Learning Agile Locomotion on Risky Terrains
- 2025Whole-Body Constrained Learning for Legged Locomotion via Hierarchical Optimization
- 2024Reinforcement Learning For Quadrupedal Locomotion: Current Advancements And Future Perspectives
- 2025Safety-Aware Reinforcement Learning for Control via Risk-Sensitive Action-Value Iteration and Quantile Regression