Dynamics and Precision Control of Tumbling Multibody Systems

Abstract

Tumbling is an inherently nonlinear phenomenon, and this paper uses a generic model of a tumbling multibody system made up of a rigid body to which discrete masses are attached; it obtains the equations of motion of the system explicitly, exhibiting the highly nonlinear nature of the dynamics. Particularizations of the generic model used here are useful in applications such as liquid sloshing in rockets, biodynamics, and capture and refurbishing of space debris. It is assumed that the mathematical description of the system is accurately known. A uniform analytical dynamics-based approach is used to obtain both the equations of motion of the system as well as the requisite control torques and forces to satisfy control requirements. No linearizations or approximations of the nonlinear dynamics are made, and closed-form controls are obtained that precisely track user-specified time-dependent control requirements on the tumbling multibody system. The methodology is demonstrated using two examples of tumbling systems with internal degrees of freedom in a constant gravity field that possess significant nonlinear internal motions. Precision tumbling control of such tumbling-vibrating multibody systems is achieved with considerable ease, making the approach presented herein useful for real-time control.

Iterative Learning‐Based PID Precision Control for Sports Performance Analysis

“…Because the instantaneous change rate of the deviation input is very large, the differential control effect is very strong, and then the differential control effect will quickly weaken. The following will analyze and study the traditional PID control principles and parameter tuning methods [10]. So, we want a kind of controller that can change the parameters according to the actual situation to control him, this kind of controller is also called adaptive controller, and we can use fuzzy PID to realize it.…”

Contact constraints-based dynamic manipulation control of the multi-fingered hand robot: a force sensorless approach

“…It is one of the frontier concepts initially proposed by Udwadia in [32][33][34][35][36][37][38][39]. Then, the constraint-following control is considered as an appealing and specialized control method for the nonlinear mechanical systems, which are discussed in a few recent research works [35][36][37][38][39][40][41][42][43][44][45]. It can investigate the intrinsic nature of the mechanical system dynamics and use the servo constraints force model to design the control.…”

Pose Tracking Control for Spacecraft Proximity Operations Using the Udwadia-Kalaba Framework

“…The Udwadia-Kalaba equation provides an elegant solution for the constrained acceleration, derived from the holonomic and non-holonomic Pfaffian constraints, that can be utilized to generate the exact real-time force commands. The control scheme uses the idea that control is a constraint on the states of a system to construct a second order constraint error dynamics equation that ensures that the states settles onto the desired control constraint surface while obeying the set performance characteristics [43,44].…”

“…Specifically, a recent advancement in analytical dynamics, the Udwadia-Kalaba equation [42] and its application in solving constrained motion is discussed. A recent work by Koganti and Udwadia [44] on real-time control of such complex constrained systems with asymptotically diminishing error dynamics using the UKE framework is also reviewed. The purpose of this section is to build the strong theoretical foundation upon which the reader would find comfort in understanding the Udwadia-Kalaba equationbased stand-off pose tracking formulation.…”

“…In its fundamental sense, control is a constraint on the state of the system. This idea was exploited in the work by Koganti and Udwadia [44] to generate desired force commands to achieve a specific control action of a multi-body system. Once a constraint equation is formulated, it is easy to incorporate it into the Udwadia-Kalaba equation to generate the exact real-time force commands that can achieve the desired trajectory with the set control performance characteristics.…”