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

Safe navigation for mobile robots demands policies that remain reliable under the high-consequence perception uncertainty of cluttered environments. Yet most existing safe reinforcement learning (RL) methods assess safety through average cumulative cost. Such metrics can mask dangerous tail-risk behaviors. To address this, we propose a framework that trains risk-sensitive policies through Conditional Value-at-Risk (CVaR) constrained optimization on an off-policy TD3 backbone and evaluates their safety margins post-training through neural network reachability verification. During training, the policy is optimized under CVaR constraints on cumulative costs, promoting sensitivity to high-cost tail outcomes rather than average behavior alone. After training, we compute action reachable sets under bounded observation uncertainty using Taylor Model analysis, yielding a safety rate metric that quantifies the proportion of evaluated states at which the policy's reachable action set remains within prescribed safety margins. A key finding is that policies trained with CVaR constraints maintain larger safety margins from obstacles across evaluated states. This makes them significantly more amenable to formal reachability verification. Experiments across ten navigation scenarios and six baselines show that our method achieves a 98.3% success rate, the highest safety verification rate among all compared methods, while revealing that average cost rankings and reachability-based safety rankings can diverge. This indicates that reachability verification captures risks which are missed by empirical cost metrics alone. We further validate our approach on a physical Clearpath Jackal robot, demonstrating successful sim-to-real transfer.

Efficiently learning safe and agile quadruped navigation in densely cluttered environments remains difficult: existing methods often lack safety and agility, or become conservative in complex scenes and require long training schedules. We propose SEA-Nav (Safe, Efficient, and Agile Navigation), a safe reinforcement learning framework for quadruped navigation in cluttered environments. A differentiable control barrier function (CBF) shield constrains the policy to produce safe velocity commands. An adaptive collision-state initialization mechanism increases the probability of learning from safety-critical near-collision experience. An action regularization term further suppresses infeasible commands for physical deployment. The policy converges after about one hour of training on a single RTX 4090 and transfers zero-shot to real-world cluttered scenes.

Robots operating in human-centered environments must safely navigate among multiple dynamic obstacles to avoid collisions with people and surrounding infrastructure. Control barrier functions (CBFs) provide an effective mechanism for safety filtering, and recent CBF-based reinforcement learning (RL) methods embed such safety information into learned policies. However, executing only safety-filtered actions during training can restrict policy exploration, a limitation that becomes particularly consequential in dynamic scenes where safety depends on relative robot-obstacle motion. We propose DODGER, a safety-guided RL framework that directly executes policy-generated actions to drive training rollouts while using CBF-filtered references and constraint violations to shape the policy toward collision-avoidance behavior. We evaluate DODGER through a Dubins-car safety analysis and demonstrate goal-directed navigation among multiple dynamic obstacles in full-order humanoid simulation and real-world humanoid experiments using LiDAR-based perception, without a runtime safety filter.