# C-STEP: Continuous Space-Time Empowerment for Physics-informed Safe Reinforcement Learning of Mobile Agents

arXiv: https://arxiv.org/abs/2603.24241 · HTML: https://mlsanity.com/paper/2603.24241/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agent threats, guardrails and governance, one of 16 directions in LLM agents and tool use.
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Placed in

- LLM agents and tool use / [Agent threats, guardrails and governance](https://mlsanity.com/agents/agent-threats-guardrails-and-governance/)
- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 10 of 10)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Variational Information Maximisation for Intrinsically Motivated Reinforcement Learning](https://mlsanity.com/paper/1509.08731/) (2015)
- [Empowerment -- an Introduction](https://mlsanity.com/paper/1310.1863/) (2013)
- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [Changing the Environment Based on Empowerment as Intrinsic Motivation](https://mlsanity.com/paper/1406.1767/) (2014)
- [Optimal Transport Perturbations for Safe Reinforcement Learning with Robustness Guarantees](https://mlsanity.com/paper/2301.13375/) (2023)
- [Hierarchical Empowerment: Towards Tractable Empowerment-Based Skill Learning](https://mlsanity.com/paper/2307.02728/) (2023)
- [Experimental Evidence that Empowerment May Drive Exploration in Sparse-Reward Environments](https://mlsanity.com/paper/2107.07031/) (2021)

## Abstract (arXiv)

Safe navigation in complex environments remains a central challenge for reinforcement learning (RL) in robotics. This paper introduces Continuous Space-Time Empowerment for Physics-informed (C-STEP) safe RL, a novel measure of agent-centric safety tailored to deterministic, continuous domains. This measure can be used to design physics-informed intrinsic rewards by augmenting positive navigation reward functions. The reward incorporates the agents internal states (e.g., initial velocity) and forward dynamics to differentiate safe from risky behavior. By integrating C-STEP with navigation rewards, we obtain an intrinsic reward function that jointly optimizes task completion and collision avoidance. Numerical results demonstrate fewer collisions, reduced proximity to obstacles, and only marginal increases in travel time. Overall, C-STEP offers an interpretable, physics-informed approach to reward shaping in RL, contributing to safety for agentic mobile robotic systems.