In a company, daily operations involve interaction between robots and humans. Specifically, two robots are responsible for transporting objects from one location to another, allowing humans to focus on less mechanical tasks. The primary objective of the robots is to move an object from an initial position to a final destination while avoiding collisions with any surrounding objects or machinery. Additionally, to ensure secure grasping of the object and prevent it from sliding, the robots must maintain a specified distance from each other.
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However, one of the robots occasionally experiences malfunctions, resulting in slight deviations in its direction of movement. Specifically, the robot has a 70% probability of maintaining the desired direction, a 20% probability of deviating to the left, and a 10% probability of deviating to the right.
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To better visualize the scenario, consider a grid of hexagonal cells representing the environment. Initially, both robots are positioned one cell apart, with the object located between them—this is the desired configuration that must be preserved. At each time step, each robot can move in one of six directions, corresponding to the six adjacent cells.
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The cost function will account for not only the time steps taken but also the time lost due to collisions between the robots and obstacles. Additionally, it will factor in the cost associated with the distance between the robots. It is important to note that if the malfunctioning robot collides with an obstacle, it will remain stationary for one time step (one second).
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The goal is to determine an optimal policy that minimizes the total time required to complete the task.
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For simplicity, we will assume a two-dimensional environment, where the object does not collide with obstacles and the two robots can occupy the same cell without it being considered a collision.
Cooperative Robots
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