Generating Stable Repetitive Motion of Underactuated Robotic Systems Using Large-Amplitude Short-Duration Control Forces

This project will promote the progress of science and advance the national prosperity and national defense, by studying generation of stable repetitive motion for underactuated robotic systems. Underactuated mechanical systems are those that have fewer control inputs than the number of their degrees-of-freedom. Underactuation appears naturally in many systems such as missiles, satellites, underwater vehicles and biped robots.

Repetitive motion is very common in underactuated robotic systems that undergo locomotion, such as underwater vehicles and biped robots, and maintaining stability is paramount for safe and reliable operation. The objective of this research is to generate stable repetitive motion of underactuated robotic systems by incorporating large-amplitude, short-duration control forces, commonly referred to as impulsive forces.

Although the effect of impulsive forces has been studied in diverse dynamical systems, the majority of the studies have been limited to theoretical investigations. This research will have a significant experimental component and will translate impulsive control of dynamical systems from theory to practice by addressing the challenges of implementation.

In addition to scientific and technological advances, this project will have broad impact through integration of research and education, diversity, and outreach. The project will provide research experience for undergraduate students and dissertation topics for graduate students and thereby contribute towards the development of the future generation of engineers and academics.

Repetitive motion is common in underactuated robotic systems and their ability to reject disturbances depends on the stability property of the orbit. This research will eliminate the limitations of current approaches to orbital stabilization of underactuated systems by including impulsive inputs in the set of admissible controls. For underactuated systems that are not subjected to impact, current approaches require controllability of the system to be checked at every point on the orbit and controller gains to be computed online by solving a periodic Ricatti differential equation.

The approach in this research, which uses both continuous and impulsive inputs, will result in a linear time-invariant system and reduce the computational cost and complexity of control design. It will also allow estimation of the region of attraction around the orbit, which will be used to determine the optimal location for application of the impulsive inputs.

To consider systems that are subjected to impact, the research will focus on bipeds, where both continuous and impulsive inputs will be used for gait stabilization; and the devil-stick, where only impulsive inputs will used. For bipeds, current approaches use numerical methods to search for stable gaits. This research will design nominal gaits analytically.

It will be possible to easily check the stability and controllability of a nominal gait and tune controller parameters to obtain controllable gaits. Impact-free nominal gaits will ensure that energy loss and hardware wear and tear due to impact will be minimized. For the devil-stick, purely impulsive control will be designed for a variety of juggling problems.

The analytical and experimental investigations will lead to new modalities of non-prehensile manipulation.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.