PRISM: Polynomial representations boost robot motor control without extra sensors

Robot policies typically rely on multilayer perceptrons (MLPs) that map observations to actions, but they miss critical cues arising from interactions among physical variables—like power, inertial effects, slip, and compliance. PRISM (Polynomial Representations for Interaction-Structured Motor Control) replaces the final layer of an MLP with a factorized polynomial module that explicitly learns these higher-order interactions. The module is gradually activated during training, allowing standard reinforcement learning backbones to stay intact while capturing contact dynamics. In imitation learning, PRISM swaps linear proprioceptive conditioning in Diffusion Policy for a polynomial layer, enabling end-to-end training of interaction-aware features.

Across humanoid locomotion and contact-rich manipulation benchmarks, PRISM consistently outperforms both standard MLP policies and larger MLPs with the same parameter count. The key insight: interaction structure cannot be replaced by simply adding capacity. More strikingly, PRISM enables sensorless compliant behavior—robots can adapt to contact forces without any force/torque sensors, tactile feedback, contact labels, or explicit admittance control. This suggests that polynomial representations should become a standard architectural choice for embodied motor control, reducing hardware costs while improving robustness in real-world tasks like assembly or legged locomotion.