Learning to Nudge: A Scalable Barrier Function Framework for Safe Robot Interaction in Dense Clutter

TL;DR

This paper tackles safe robot interaction in densely cluttered environments where physical contact is unavoidable. It proposes Dense Contact Barrier Functions (DCBF), an implicit-interaction, object-centric, composable safety framework trained offline on a small set of objects and deployed online as a single global safety filter, $B_{global} = \\min_i B(\boldsymbol{r}^{t}_{i}, oldsymbol{O}^{t-1}_{i})$, that scales with the number of objects. Key contributions include an implicit interaction CBF formulation, a composable per-object barrier with object-centric representation, and a refinement procedure to reduce conservativeness, all validated in simulation to enable collision-free navigation and safe, contact-rich manipulation across dense scenes. The results demonstrate strong generalization to up to 40 objects without retraining and highlight the practical potential for deploying safe contact-enabled robots in unstructured environments. Overall, DCBF provides a scalable, task-agnostic safety mechanism bridging traditional collision avoidance and contact-rich manipulation for real-world robotics.

Abstract

Robots operating in everyday environments must navigate and manipulate within densely cluttered spaces, where physical contact with surrounding objects is unavoidable. Traditional safety frameworks treat contact as unsafe, restricting robots to collision avoidance and limiting their ability to function in dense, everyday settings. As the number of objects grows, model-based approaches for safe manipulation become computationally intractable; meanwhile, learned methods typically tie safety to the task at hand, making them hard to transfer to new tasks without retraining. In this work we introduce Dense Contact Barrier Functions(DCBF). Our approach bypasses the computational complexity of explicitly modeling multi-object dynamics by instead learning a composable, object-centric function that implicitly captures the safety constraints arising from physical interactions. Trained offline on interactions with a few objects, the learned DCBFcomposes across arbitrary object sets at runtime, producing a single global safety filter that scales linearly and transfers across tasks without retraining. We validate our approach through simulated experiments in dense clutter, demonstrating its ability to enable collision-free navigation and safe, contact-rich interaction in suitable settings.

Figures (4)

• Figure 1: Simulated Robot trajectory from start to goal across different methods. The first row shows the Do Nothing baseline, where the robot directly pushes through the clutter, causing multiple objects to be knocked over. Interacted objects are highlighted in red, with the object starting closest to the end-effector shown in dark red and others in light red. The second row shows our proposed method, which safely interacts with objects to reach the goal without violating safety. Interacted objects are highlighted in green, with the starting closest object shown in dark green and others in light green. The third row plots the tilt angles of the interacted objects over time, with curves matching the same color coding (dark/light red and dark/light green) with a dashed line denoting the safety threshold, $15\degree$. The red curves exceed tilt threshold, indicating safety violations, whereas the green curves remain below the threshold, demonstrating safe interactions.
• Figure 2: Comparison of safe boundaries for the initial model and refined model ($\sigma=0.01$): (a) Environment snapshot with contact. The end-effector makes slight contact with a bottle, pushing it by a small angle while keeping it within the safe region. (b) Global CBF value plot for the initial model under contact. The conservative boundary incorrectly treats the interaction as unsafe, often leading to the robot stalling. (c) Global CBF value plot for the refined model under contact. The boundary accommodates safe interactions, reflecting less conservative, realistic reasoning about safety for dense environments
• Figure 3: Safe and success rate of different methods evaluated across environments with increasing object density ($4$, $10$, $20$, and $40$ objects). This metric illustrates percentage of trajectories where the robot both reached the goal and stayed safe throughout the trajectory. Results are computed over $100$ randomized trajectories for each method in each environment. The results highlight the limitations of the baselines, especially at higher object densities and the robustness of our method in maintaining both safety and task success.
• Figure 4: Performance of different methods in environments of varying object densities ($4$, $10$, $20$ and $40$ objects). The Safe Rate measures the percentage of safe trajectories (higher is better), and the Average Final Distance to Goal measures final distance to the target (lower is better). These metrics were computed over the same experiment shown in Fig. \ref{['fig:safe_reach_success_rate']}, and provide further insight into the performance of each method. These results highlight the limitations of baselines (Do Nothing, Backstepping) in staying safe, the conservativeness of APF, the conservativeness of the Initial Model at higher densities, and the robustness of our proposed method, balancing safety and task success.