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Constructive Control Tools for Legged Robots
On a macroscopic level, locomotion on land can be understood based on a few principles, including mechanisms of energy exchange, stability and maneuverability. Central to this macroscopic view is the introduction of archetypal reductive models, capable of capturing the primary characteristics of the task-level behavior, e.g., walking or running. The Spring Loaded Inverted Pendulum (SLIP) is one such model; it has been proposed as a canonical model of the center of mass dynamics of running animals and robots. Notwithstanding its apparent simplicity, the SLIP has been invaluable in uncovering basic principles of running in animals, and in synthesizing empirical control laws for running robots. Unfortunately, reductive models like the SLIP provide no information on the control mechanisms governing the coordination of the multiple joints and limbs of the high-degree-of-freedom-plant in order to produce the observed behavior. The coordinated recruitment of the plant into a low-degree-of-freedom target model constitutes the central problem addressed in my work, which aims at offering a mathematically precise feedback control solution to this problem.
To explore the potential of these ideas, the robotic monopod Thumper has been constructed in a collaborative effort between the University of Michigan and Carnegie Mellon University. The control law proposed for Thumper grew out of rigorous nonlinear controller synthesis ideas, such as the Hybrid Zero Dynamics (HZD) framework, and was originally developed based on an approximation of Thumper's dynamics, termed the Asymmetric Spring Loaded Inverted Pendulum (ASLIP). The proposed control approach coordinates the actuated degrees of freedom of the robot plant so that a lower-dimensional hybrid system, i.e., a reductive model that encodes the desired running behavior, emerges from the closed-loop dynamics. This lower-dimensional system governs the behavior of the robot. The control design procedure is systematic, rendering this framework an attractive alternative to traditional heuristic approaches for controlling legged robots by avoiding laborious trial-and-error procedures during experimental implementation.
The monopod Thumper The Asymmetric Spring Loaded Inverted Pendulum

Representative publications