Doctoral Defense - Aakash Khandelwal

The Department of Mechanical Engineering

Michigan State University

Ph.D. Dissertation Defense

Friday, September 26, 2025 at 1:30 PM EDT

Engineering Building Room 3540

 

ABSTRACT

IMPULSIVE CONTROL FOR ORBITAL STABILIZATION AND NONPREHENSILE MANIPULATION

By: Aakash Khandelwal

Advisor: Dr. Ranjan Mukherjee

Several dynamical systems are underactuated, i.e., have fewer control inputs than the minimum number of generalized coordinates needed to describe the system. Underactuated dynamics arise commonly in legged robots, and in the study of robotic nonprehensile manipulation, which is manipulation of objects without grasping. The dynamics of such systems may additionally be hybrid and nonlinear. Many applications of underactuated systems require stable, repetitive motion; the problem of realizing such motion is challenging owing to the limited control inputs available. Impulsive control is shown to be an effective, and sometimes necessary, tool in stabilizing and transitioning between periodic orbits for underactuated systems.

Gait design and stabilization for bipeds is an important control problem in underactuated systems. The problem of designing and stabilizing impact-free gaits for planar bipeds is addressed by defining a set of geometric constraints that eliminate foot-ground impact forces at the time of leg interchange. It is shown that a family of stable gaits, whose stride length and walking speed can be independently chosen, is guaranteed to exist. The efficacy of continuous and impulsive control, working in tandem, in stabilizing a desired gait and transitioning between distinct gaits is demonstrated.

Nonprehensile manipulation of the devil-stick is investigated extensively. The devil-stick represents an extended object, described by orientation in addition to position, and controlling its motion without grasping is a challenging problem. Various underactuated devil-stick manipulation tasks are considered, including propeller motion using continuous forcing, and juggling using impulsive inputs. Devil-stick juggling in three dimensions is addressed by transforming the control problem to one of fixed point stabilization in a rotating reference frame. By varying the fixed point gradually with time, it is shown that a variety of maneuvers can be achieved. To address more complex underactuated juggling tasks, the concept of discrete virtual holonomic constraints is introduced. At the discrete instants when impulsive inputs are applied, the location of the center-of-mass of the devil-stick is specified in terms of its orientation angle. This yields the discrete zero dynamics, which provides conditions for stable juggling. An impulsive control design that enforces the discrete virtual holonomic constraint, and stabilizes a desired juggling motion is presented. The approach is studied in the context of propeller motion and planar juggling of the devil-stick.

For experimental implementation of devil-stick juggling, the mechanics of impact on circular beams is investigated using a finite element approach that captures energy transfer to vibration modes. Simulations and experiments show spatial variation of the coefficient of restitution for impacts along the length of a pinned beam. A pinned beam is juggled using a general-purpose robot by synchronizing the motion of the robot directly to that of the beam using virtual holonomic constraints. The impact location on the beam and the velocity of the robot end-effector at impact are chosen based on the coefficient of restitution. Juggling in the presence of losses, delays, uncertainties, and hardware constraints is demonstrated.