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Learning to Play Cup-and-Ball with Noisy Camera Observations

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Document pages: 6 pages

Abstract: Playing the cup-and-ball game is an intriguing task for robotics researchsince it abstracts important problem characteristics including systemnonlinearity, contact forces and precise positioning as terminal goal. In thispaper, we present a learning model based control strategy for the cup-and-ballgame, where a Universal Robots UR5e manipulator arm learns to catch a ball inone of the cups on a Kendama. Our control problem is divided into twosub-tasks, namely $(i)$ swinging the ball up in a constrained motion, and$(ii)$ catching the free-falling ball. The swing-up trajectory is computedoffline, and applied in open-loop to the arm. Subsequently, a convexoptimization problem is solved online during the ball s free-fall to controlthe manipulator and catch the ball. The controller utilizes noisy positionfeedback of the ball from an Intel RealSense D435 depth camera. We propose anovel iterative framework, where data is used to learn the support of thecamera noise distribution iteratively in order to update the control policy.The probability of a catch with a fixed policy is computed empirically with auser specified number of roll-outs. Our design guarantees that probability ofthe catch increases in the limit, as the learned support nears the true supportof the camera noise distribution. High-fidelity Mujoco simulations andpreliminary experimental results support our theoretical analysis.

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