Udwadia–Kalaba constraint-based tracking control for artificial swarm mechanical systems: dynamic approach

Zhao, Ruiying; Li, Meng; Niu, Qian; Chen, Ye‐Hwa

doi:10.1007/s11071-020-05613-7

Cited by 42 publications

(21 citation statements)

References 26 publications

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“…Theorem 4 Consider the mechanical system (1) and the desired equality constraint (2) and inequality constraint (10). Suppose Assumptions 1, 2 and the First Postulate of Constraint are met.…”

Section: Equation Of Motion With Equality and Inequality Constraintsmentioning

confidence: 99%

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An Alternative Modeling and Control Approach for Fixed Boundary Motion Requirement in Industrial Automation and Robotics Using Constraint Following Method

Zhang

Zhao

Chen

et al. 2022

Preprint

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In industrial automation and robotics, the motion control of the automatic equipment (e.g., mobile robots, assembling manipulators, machine tools, etc.) is an important task for intelligent and flexible manufacturing. Because of the limited space on the factory floor and limited operating conditions, most tasks require work in confined spaces and subject to regulatory requirements. This confined motion control objective is considered as the constraints in the paper (hence, it belongs to the constraint following control field). There are two categories of constraints for the motion control: equality and inequality which are corresponding to the two motion requirements. The problem of motion requirement with fixed boundary has not been solved systematically using constraint following method. The equation of motion for a constrained mechanical system which addresses both constraints is presented. This can be considered a generalization of the Udwadia-Kalaba (U-K) equation. The advantages of the equation include that it does not require additional pseudo variables and the solution is analytical. This exhibits profound applications. As a demonstration, a pan/tilt device mounted under the firefighting unmanned aerial vehicles (UAVs) is manipulated. The water-jet nozzle need motion requirements of swaying horizontally and not overshooting limits in vertical. Simulation and experimental results are presented to validate the effectiveness of the proposed approach.

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Section: Equation Of Motion With Equality and Inequality Constraintsmentioning

confidence: 99%

“…Based on the U-K equation, take the motion requirements as constraints, the constraint following control has been presented [8][9][10][11] in motion control. The advantage of this method is that we only need to list the constraint equation corresponding to the desired trajectory [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

An Alternative Modeling and Control Approach for Fixed Boundary Motion Requirement in Industrial Automation and Robotics Using Constraint Following Method

Zhang

Zhao

Chen

et al. 2022

Preprint

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

Yang

et al. 2021

Nonlinear Dyn

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A novel analytical modeling and dynamic manipulation control method of the multi-fingered hand robot has been proposed in the paper. Based on the contact constraints, the explicit dynamics modeling of the hand robot manipulating an object is hierarchically established by Udwadia-Kalaba equation with no auxiliary variable (e.g., Lagrange multipliers or quasi-generalized variables). Through the second order of the contact constraints, the grasping forces of the hand robot in the manipulation work space are derived explicitly and decoupled with the control torques of the finger joints. Consider the hand robot and the object as an entire system in the control design. Motivated by Udwadia's work, the manipulation task of the grasped object is novelly used to formulate a set of servo constraints. In virtue of following the servo constraints, the hand robot can manipulate the object to accomplish the desired task. With the formulated contact forces model, a model-based dynamic control method is proposed for the hand robot to handle the object, which does not depend on the force feedback from the fingertips sensors (force sensorless). The system performance under

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“…Different from previous research, the Udwadia–Kalaba theory does not adopt linearization or approximations. A series of dynamic system control based on the Udwadia–Kalaba method is designed, including robust control, adaptive robust control, and optimal design of robust control (Chen et al, 2020; Dong et al, 2018; Sun, 2017; Wu et al, 2020; Yu et al, 2020; Zhao et al, 2020). Trajectory tracking control of the mobile robot is also realized based on the Udwadia–Kalaba approach (Sun et al, 2016; Yu et al, 2016), but the system’s initial conditions must satisfy the desired constraints, which may not really occur for various factors.…”

Section: Introductionmentioning

confidence: 99%

A hierarchical constraint approach for dynamic modeling and trajectory tracking control of a mobile robot

Ding

Tian

et al. 2021

Journal of Vibration and Control

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The dynamic modeling and trajectory tracking control of a mobile robot is handled by a hierarchical constraint approach in this study. When the wheeled mobile robot with complex generalized coordinates has structural constraints and motion constraints, the number of constraints is large and the properties of them are different. Therefore, it is difficult to get the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. To solve the aforementioned problem, a creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed. In this approach, constraints are classified into two levels, structural constraints are the first level and motion constraints are the second level. In the second level constraint, arbitrary initial conditions may cause the trajectory to diverge. Thus, we propose the asymptotic convergence criterion to deal with it. Then, the analytical dynamic equation and trajectory tracking control force of the wheeled mobile robot can be obtained simultaneously. To verify the effectiveness and accuracy of this methodology, a numerical simulation of a three-wheeled mobile robot is carried out.

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Udwadia–Kalaba constraint-based tracking control for artificial swarm mechanical systems: dynamic approach

Cited by 42 publications

References 26 publications

An Alternative Modeling and Control Approach for Fixed Boundary Motion Requirement in Industrial Automation and Robotics Using Constraint Following Method

An Alternative Modeling and Control Approach for Fixed Boundary Motion Requirement in Industrial Automation and Robotics Using Constraint Following Method

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

A hierarchical constraint approach for dynamic modeling and trajectory tracking control of a mobile robot

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