Riding the Shifting Potential: When Reactive Control Suffices for Multi-Goal Behavior
This work challenges the assumption that reactive control is insufficient for multi-goal behavior, offering a simple method that resolves local minima without demonstrations or retraining.
The authors show that reactive control can handle multi-objective tasks by using nullspace projections in a graph-based world model, achieving 100% success in planar pushing tasks where baselines fail (0% for steepest descent, ~55% for diffusion policy).
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.