We present a learning and control strategy that enables robots to harness physical human interventions to update their trajectory and goal during autonomous tasks. Within the state of the art, the robot typically reacts to physical interactions by modifying a local segment of its trajectory, or by searching for the global trajectory offline, using either replanning or previous demonstrations. Instead, we explore a one-shot approach: here, the robot updates its entire trajectory and goal in real

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... time without relying on multiple iterations, offline demonstrations, or replanning. Our solution is grounded in optimal control and gradient descent, and extends linear-quadratic regulator controllers to generalize across methods that locally or globally modify the robot's underlying trajectory. In the best case, this Linear-quadratic regulator + Learning approach matches the optimal offline response to physical interactions, and-in more challenging cases-our strategy is robust to noisy and unexpected human corrections. We compare the proposed solution against other real-time strategies in a user study and demonstrate its efficacy in terms of both objective and subjective measures. INTRODUCTION Our work seeks to leverage physical human-robot interaction (pHRI) to adapt robot behavior during the current task. We treat physical interactions as a method for conveying information, which the human can use to communicate his or her desired behavior to the robot. Consider a personal robot that is setting the table for a human end user: this robot may not know the right location to place a plate or the right way to move that plate to the goal. The human can physically interveneby applying forces and torques-and correct the robot's behavior, such as pushing the robot towards the table or guiding the robot away from the stove. Our research develops robotic controllers that