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The Dubins Car and Other Arm-Like Mobile Robots

This paper investigates the connection between the kinematics of robots arms and the shortest paths for mobile robots. Lagrange multipliers are used to show that the shortest paths are equivalent to arms in configurations that balance an external force, while applying equal torques and forces at each joint. Analysis of the arm Jacobian yields a further geometric interpretations of optimal paths, constraining the locations of rotation centers and the directions of translations that may occur along optimal paths.