# SafeMind: A Risk-Aware Differentiable Control Framework for Adaptive and Safe Quadruped Locomotion

arXiv: https://arxiv.org/abs/2604.09474 · HTML: https://mlsanity.com/paper/2604.09474/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [RMA: Rapid Motor Adaptation for Legged Robots](https://mlsanity.com/paper/2107.04034/) (2021)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [LM-Nav: Robotic Navigation with Large Pre-Trained Models of Language, Vision, and Action](https://mlsanity.com/paper/2207.04429/) (2022)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Control Barrier Functions for Stochastic Systems](https://mlsanity.com/paper/2003.03498/) (2020)
- [Learning Robust Hybrid Control Barrier Functions for Uncertain Systems](https://mlsanity.com/paper/2101.06492/) (2021)
- [MBMF: Model-Based Priors for Model-Free Reinforcement Learning](https://mlsanity.com/paper/1709.03153/) (2017)

## Abstract (arXiv)

Learning-based quadruped controllers achieve impressive agility but typically lack formal safety guarantees under model uncertainty, perception noise, and unstructured contact conditions. We introduce SafeMind, a differentiable stochastic safety-control framework that unifies probabilistic Control Barrier Functions with semantic context understanding and meta-adaptive risk calibration. SafeMind explicitly models epistemic and aleatoric uncertainty through a variance-aware barrier constraint embedded in a differentiable quadratic program, thereby preserving gradient flow for end-to-end training. A semantics-to-constraint encoder modulates safety margins using perceptual or language cues, while a meta-adaptive learner continuously adjusts risk sensitivity across environments. We provide theoretical conditions for probabilistic forward invariance, feasibility, and stability under stochastic dynamics. SafeMind is deployed on Unitree A1 and ANYmal C at 200~Hz and validated across 12 terrain types, dynamic obstacles, morphology perturbations, and semantically defined tasks. Experiments show that SafeMind reduces safety violations by 3--10x and energy consumption by 10--15% relative to state-of-the-art CBF, MPC, and hybrid RL baselines, while maintaining real-time control performance.