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Motion Planning

Modified 2018-11-15 by Stefanie Tellex

This unit focuses on the problem of motion planning for robotics. This is the problem of moving through space without colliding. It typically abstracts sensing and perception and assumes perfect ability to move in the space. The problem is to find a trajectory through the space for the robot (which may be a drone, a vehicle or an arm) that avoids collisions.

Formally, the input to motion planning is the model of the robot, a model of obstacles in the environment, and a start state, and a goal state. The output is a trajectory through space that causes the robot to move from start state to goal state without colliding with obstacles in its environment. A real-life example of motion planning is when a person parallel parks a car. This trajectory is not obvious, and takes time to learn, because of the car’s movement constraints.

Avoiding obstacles is a key part of robotics. The Skydio drone’s advance over the state-of-the-art was its ability to accurately detect and avoid obstacles in its environment. In our work so far with the drone, we have modeled the robot as a point, and ignored obstacles. Indeed, the drone does not have sensors pointed in any direction but downwards and has no awareness of obstacles in its environment. However we will model this problem by creating virtual obstacles that the drone will avoid as it flies.

A second important domain for motion planning is robotic arms. A robotic arm is modeled as a number of joints and arm geometry. Each joint is parameterized as a joint angle (and in general, joint velocity). This parameter can be set to move the arm to a particular joint, and read using joint encoders. Given the joint states and arm geometry, we can compute the end effector pose. This problem is called forward kinematics and has a closed form solution. We would also like to solve the inverse problem: given an end effector pose we would like to find joint states that result in the end effector attaining that position. This problem is called inverse kinematics and does not have a closed form solution.