Control of Robots that Move by Leaping, Bouncing, and Swinging

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A wide variety of robotic tasks, including locomotion and manipulation, can be characterized by switches between different sets of contact conditions. For example, a biped running robot can have its left foot on the ground, its right foot on the ground, or no feet on the ground. The equations of motion of the robot, which govern how the forces and torques of the motors at the robot's joints cause the robot to move, change as the robot changes contacts with the ground. These switching equations raise a number of open questions in motion planning and control for dynamically locomoting legged robots, such as robotic pack mules being tested by the US Army and a new generation of humanoid robots being developed around the world. Control theory, the basis of the lowest-level software that controls these robots, has not kept up with the latest developments in robot design. This research will narrow that gap, providing a firm theoretical "footing" for the software controlling dynamically locomoting robots. This will help realize the vision of legged robots in military, service, and home applications. The research will also provide opportunities for undergraduates and graduate students to demonstrate their work at the Chicago Museum of Science and Industry, influencing the next generation of scientists and engineers.This project focuses on the management of energy, momentum, and uncertainty for uncertain hybrid mechanical control systems with impacts. While the classical goal of robot motion control is to control the state of the robot with zero uncertainty, this research deals explicitly with the fact that this goal is idealized for all uncertain hybrid systems with impact and formally impossible for many due to their underactuation. The methodology applies to a broad class of Lagrangian control systems with impacts, with a focus on locomotion systems. The work will establish establish principles of state belief propagation and filtering, belief controllability, motion planning, and feedback control for systems with the structure of uncertain hybrid mechanical systems with impacts.