Safe Stochastic Explorer: Enabling Safe Goal Driven Exploration in Stochastic Environments and Safe Interaction with Unknown Objects

TL;DR

Safe Stochastic Explorer addresses safe goal‑driven exploration in unknown environments with inherently stochastic dynamics by learning the unknown safety function $q(x)$ with Gaussian Processes and enforcing probabilistic safety bounds. The framework provides discrete, continuous, and object‑centric formulations, introducing refinement operators $ar{R}$ and $\bar{m}$ to expand safe sets while maintaining returnability and safe arrivals under uncertainty. Empirical results in simulation and hardware demonstrate reduced safety violations and reliable goal attainment when accounting for stochastic transitions, outperforming baselines that neglect stochasticity. This work advances autonomous robot safety in unstructured settings and enables safe interaction with unknown objects, with broad implications for planetary exploration, warehouses, and home robotics.

Abstract

Autonomous robots operating in unstructured, safety-critical environments, from planetary exploration to warehouses and homes, must learn to safely navigate and interact with their surroundings despite limited prior knowledge. Current methods for safe control, such as Hamilton-Jacobi Reachability and Control Barrier Functions, assume known system dynamics. Meanwhile existing safe exploration techniques often fail to account for the unavoidable stochasticity inherent when operating in unknown real world environments, such as an exploratory rover skidding over an unseen surface or a household robot pushing around unmapped objects in a pantry. To address this critical gap, we propose Safe Stochastic Explorer (S.S.Explorer) a novel framework for safe, goal-driven exploration under stochastic dynamics. Our approach strategically balances safety and information gathering to reduce uncertainty about safety in the unknown environment. We employ Gaussian Processes to learn the unknown safety function online, leveraging their predictive uncertainty to guide information-gathering actions and provide probabilistic bounds on safety violations. We first present our method for discrete state space environments and then introduce a scalable relaxation to effectively extend this approach to continuous state spaces. Finally we demonstrate how this framework can be naturally applied to ensure safe physical interaction with multiple unknown objects. Extensive validation in simulation and demonstrative hardware experiments showcase the efficacy of our method, representing a step forward toward enabling reliable widespread robot autonomy in complex, uncertain environments.

Figures (6)

• Figure 1: Ground Robot Environments: All $8$ environments used for the Ground Robot Experiments. In every environment, we show the robot randomly initialized within its initial safe region. The color represents the ground truth safety value (with higher values indicating more unsafe conditions), with a safety threshold of $4$ across all environments.
• Figure 2: Continuous Case Growing Stochasticity Ground Robot Experiment Results: detailed in Section \ref{['sec:continuous_case_experiments']}. The plots compare the success rate, violation rate and average states explored across increasing levels of environment noise in the Ground Robot Environments. Each individual bar captures the results across $40$ randomized trials over $8$ environments. Performance is shown for our method (blue/green) and the baseline (orange/red), using both normal and $\beta$ scaling variants. Each shade of color represents one of $3$ GP configurations. As environment stochasticity increases, our method with $\beta$ scaling maintains substantially higher success rates and lower safety violation rates in comparison to either baseline. this is further supported by the larger number of states explored before termination. $\beta$ scaling enables us to effectively manage the safety-performance tradeoff, while our base method prioritizes safety and becomes too conservative and loses performance as noise grows (though still outperforming the baselines) . Showing performance across different GP configurations demonstrates the robustness of our method, confirming that these performance trends hold across varied parameter settings.
• Figure 3: Ground Robot Trajectories: These figures depict snapshots of the ground robot trajectory and corresponding GP predicted mean safety values in top and bottom rows respectively. Sub-figures (a) and (b) depict a trajectory for the discrete case experiments (detailed in Section \ref{['sec:discrete_case_experiments']}) while (c) and (d) depict a trajectory for the continuous case experiments (detailed in Section \ref{['sec:continuous_case_experiments']}). Without accounting for stochastic transitions the baseline method quickly violates safety, exceeding the safety threshold of $4$ by entering states with safety values of $4.05$ in the discrete case and $6.94$ in the continuous case respectively. Meanwhile, by accounting for stochasticity our algorithm is able to explore the environment to find a safe path to the goal without violating safety.
• Figure 4: Safe Object Environments: All $11$ environments used for the Safe Object Experiments. In every environment, the robot is initialized within an initial safe set, having to reach its goal on the other side of the table. The object parameters are varied across each environment and the robot state space is restricted, preventing it from trivially going around the objects.
• Figure 5: Safe Object Trajectories: These figures depict snapshots of the safe object robot trajectory and corresponding GP predicted mean safety values from the Safe Object Experiments detailed in Section \ref{['sec:safe_object_experiments']}. Sub-figures (a) and (c) show trajectories using the baseline method, while (b) and (d) show our method on environments with a single and multiple rows of objects respectively. Unable to properly account for the unknown interaction dynamics with different objects, the baseline readily violates safety by excessively tipping over objects. Meanwhile, by using stochasticity to account for the unknown interactions our approach is able to safely interact with the objects, finding those that are safe to push out of the way and reach the goal without any safety violations.

Theorems & Definitions (7)

• Definition 1: Stochastic Return Refinement Operator, ${\bar{R}}$
• Definition 2: Single-step Safe Stochastic Arrival Refinement Operator, $m$
• Definition 3: Safe Stochastic Arrival Refinement Operator, $\bar{m}$
• Definition 4: Single Step Immediate safe expansion operators ${I}^{p, 1}_{t}, {I}^{o, 1}_{t}$
• Definition 5
• Definition 6: Immediate Safe Expansion Indicators ${i}^{p}_{t}, {i}^{o}_{t}$
• Definition 7: Safe Stochastic Arrival Indicators ${m}^{p}_{t}, {m}^{o}_{t}$