In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value function space, which is defined by an Eikonal partial differential equation (PDE). Therefore, our PNO model, despite being trained with a finite number of samples at coarse resolution, inherits the zero-shot super-resolution property of neural operators. We demonstrate accurate value function approximation at 16× the training resolution on the MovingAI lab’s 2D city dataset, compare with state-of-the-art neural value function predictors on 3D scenes from the iGibson building dataset and showcase optimal planning with 4-joint robotic manipulators. Lastly, we investigate employing the value function output of PNO as a heuristic function to accelerate motion planning. We show theoretically that the PNO heuristic is $\epsilon$-consistent by introducing an inductive bias layer that guarantees our value functions satisfy the triangle inequality. With our heuristic, we achieve a $30$% decrease in nodes visited while obtaining near optimal path lengths on the MovingAI lab 2D city dataset, compared to classical planning methods (A$^\ast$, RRT$^\ast$).

In this work, we address the problem of solving complex collaborative robotic tasks subject to multiple varying parameters. Our approach combines simultaneous policy blending with system identification to create generalized policies that are robust to changes in system parameters. We employ a blending network whose state space relies solely on parameter estimates from a system identification technique. As a result, this blending network learns how to handle parameter changes instead of trying to learn how to solve the task for a generalized parameter set simultaneously. We demonstrate our scheme's ability on a collaborative robot and human itching task in which the human has motor impairments. We then showcase our approach's efficiency with a variety of system identification techniques when compared to standard domain randomization. The code is available on Luke Bhan's Github.