Moving Two Objects on a 2D Plane Using an Infinitely Long Paddle
This paper determines an algorithm for pushing two objects that have specified destinations using a robot that has an infinitely long paddle. The manipulator is a robot that uses a paddle to push an object in any direction in the configuration space that is normal to the paddle. The paddle is modeled as a line with no thickness and infinite length. Since the robot’s paddle is infinitely long, all objects within the area of effect of the paddle will be pushed. The paddle can be raised, placed at any position and orientation in two-dimensions, and lowered before performing a push. Every time the paddle is raised or its orientation is changed counts as the end of a push. The paddle tries to avoid moving objects that have reached their destination. If it moves objects that have reached their destination, it can adjust to the new configuration. There are no other elements on the workspace other than the movable objects. There are no permanent obstacles on the workspace. The method implemented is a mix of combinator y math and geometry to find a symmetric solution to the problem. Using a Monte Carlo approach to testing this algorithm, it was determined that, on average, the robot only needs three pushes to finish a randomly generated case of this problem. This is an intuitive answer to this problem: 1) finish one object; 2) set up the second object; and 3) finish the second object. Depending on the initial configuration of the objects, there are situations in which the number of pushes greatly increases because of object to object interaction.