Organizations: Department of Mechanical Engineering, University of California Berkeley, Berkeley, CA 94709, USA
Abstract
Ensuring safety for black-box hybrid dynamical systems presents significant challenges due to their instantaneous state jumps and unknown explicit nonlinear dynamics. Existing solutions for strict safety constraint satisfaction, like control barrier functions (CBFs) and reachability analysis, rely on direct knowledge of the dynamics. Similarly, safe reinforcement learning (RL) approaches often rely on known system dynamics or merely discourage safety violations through reward shaping. In this work, we want to learn RL policies which provably satisfy affine state constraints in closed loop for black-box hybrid dynamical systems with affine reset maps. Our key insight is forcing the RL policy to be affine and repulsive near the constraint boundaries for the unknown nonlinear dynamics of the system, providing guarantees that the trajectories will not violate the constraint. We further account for constraint violation due to instantaneous state jumps that occur due to impacts or reset maps in the hybrid system by introducing a second repulsive affine region before the reset that prevents post-reset states from violating the constraint. We derive sufficient conditions under which these policies satisfy safety constraints in closed loop. We also compare our approach with state-of-the-art reward shaping and learned-CBF methods on hybrid dynamical systems like the constrained pendulum and paddle juggler environments. In both scenarios, we show that our methodology learns higher quality policies while always satisfying the safety constraints.
Reinforcement learning (RL) enables the synthesis of control policies directly from data, making it highly appealing for complex cyber-physical systems (CPSs) and robotics. A persistent challenge, however, is ensuring strict, hard safety constraints during the active learning phase. In real-world physical systems, violating mechanical limits can cause irreversible damage, necessitating that exploration remains strictly within safe operational regions. We propose a generalized framework that combines the adaptive, high-performance nature of deep reinforcement learning (DRL) with the formal safety guarantees of model predictive control (MPC). Using a mathematical model of the system dynamics, offline MPC computations define a feasible state-action space, representing all safe combinations of system states and control inputs that guarantee constraint satisfaction. During training and deployment, the RL agent's instantaneous actions are projected onto this globally verified feasible set via a safety filter. We systematically evaluate our generalized approach on a non-linear 1-DoF laboratory testbed, demonstrating successful exploration and stable policy convergence on physical hardware.
Ensuring safe exploration in high-dimensional systems with unknown dynamics remains a significant challenge. Existing safe reinforcement learning methods often provide safety guarantees only in expectation, which can still lead to safety violations. Control-theoretic approaches, in contrast, offer hard constraint-based safety guarantees but typically assume access to known system dynamics or require accurate estimation of control-affine models. In this paper, we propose a safe reinforcement learning framework that learns a probabilistic control-affine dynamics model in an offline setting. The learned model is leveraged to explicitly construct control barrier functions (CBFs) that incorporate model uncertainty to provide conservative safety constraints. These CBF constraints are enforced through an online constraint-based action correction mechanism, enabling safe exploration without overly restricting task performance. Empirical evaluations on nonlinear, complex continuous-control benchmarks demonstrate that our approach achieves returns comparable to those of existing baselines while significantly reducing safety violations.
Safe model-based reinforcement learning (RL) often bridges control-theoretic analysis and RL for robots to safely explore (partially) unknown system dynamics while deriving control actions for task efficiency. The control performance and safety assurance typically rely on prior knowledge of partially modeled nominal system dynamics and the data-driven models that compensate for residual model uncertainties. However, existing methods often overlook the structure of residual model uncertainties (e.g., components affine in control), which could lead to overly conservative robot behaviors or invalid safety guarantees under the safe learning-based controllers. This paper proposes a safe reinforcement learning framework that learns control-affine dynamics with a certifiable data-driven safe policy using control barrier functions (CBF). Specifically, we first use Control-Affine Random Fourier Features (ARFF) to model robot dynamics in a control-affine form, which offers computational efficiency that scales with dataset size and reduces potential model bias for model-based reinforcement learning. Then, a model-free, efficient uncertainty quantification method using adaptive conformal prediction (ACP) is applied to quantify the uncertainty in the safety constraint arising from the learned control-affine dynamics. This allows for data-driven safety assurance amenable to principled and efficient controller synthesis with CBF. Simulation results on the cartpole and the 3D quadrotor platforms demonstrate the effectiveness of the proposed framework.