Riding the Shifting Potential: When Reactive Control Suffices for Multi-Goal Behavior

2026-05-26

AI Summary

This work addresses the challenge of objective conflicts in multi-task robotic control, which often lead to local minima and cause conventional reactive controllers to fail. To resolve this, the authors propose a dynamic nullspace projection mechanism that continuously adjusts task priorities based on the current state within a graph-structured world model. Specifically, gradients of lower-priority tasks are projected into the nullspace of higher-priority tasks, enabling real-time conflict resolution. This approach overcomes fundamental limitations of static potential fields in non-convex obstacle environments and manipulation scenarios. Evaluated on non-convex navigation and planar pushing tasks, the method achieves 100% success rates—significantly outperforming steepest descent (0%) and diffusion policies (~55%)—and demonstrates successful deployment on a physical robot system.

Abstract

Reactive control is often considered insufficient for multi-objective tasks because conflicting objectives give rise to local minima. We argue this limitation is not inherent but arises from static encodings that fail to reflect how objectives currently interact. We exploit the interaction structure encoded in a graph-based world model by extending it with nullspace projections: conflicts are resolved where they arise by projecting lower-priority gradients into the nullspace of higher-priority ones, with priorities determined continuously from the current state. We demonstrate this in two domains where conflicts between objectives are central: navigation around non-convex obstacles, where static potential fields fundamentally fail, and planar pushing of non-convex objects, where our method achieves $100\%$ success across one-hundred configurations versus $0\%$ for the steepest-descent baseline and ${\sim}55\%$ for diffusion policy, without demonstrations or retraining. The same formulation transfers directly to a real robot with additional perceptual and kinematic constraints, accommodating them through the same mechanism.

Problem

• reactive control
• multi-goal behavior
• objective conflicts
• local minima
• non-convex obstacles

Innovation

• reactive control
• nullspace projection
• multi-goal behavior
• graph-based world model
• dynamic priority resolution