Equations of motion of constrained mechanical systems: given force depends on constraint force

Chen, Y.H.

doi:10.1016/s0957-4158(98)00053-1

Cited by 23 publications

(16 citation statements)

References 4 publications

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“…It also includes a number of standard control problems such as stabilization, trajectory following, and optimality. 36,37 The trajectory tracking constraint is just one of these constraints above.…”

Section: Dynamics Of the Snakementioning

confidence: 99%

“…The initial conditions q(0) = q 0 and _ q(0) = _ q 0 are required to satisfy the constraints (36). However, it is usually difficult to achieve in practical engineering applications due to various factors.…”

Section: Controller Designmentioning

confidence: 99%

“…Udwadia and colleagues [32][33][34] first made a preliminary research in the field of nonlinear mechanical systems using servo constraint control method. Chen [35][36][37][38] achieved the systematical servo constraint controller design of mechanical systems based on Udwadia's research and also studied servo constraint problem, indicating that based on Maggi equation, the required constraint inputs can be acquired by servo control. Schutte 39 studied the modeling and control problem of nonholonomic mechanical systems when using Udwadia-Kalaba equation and designed nonlinear feedback controllers for such types of mechanical system, and Bajodah et al 40 focused on the mathematical calculation problems in servo control solution when using Udwadia-Kalaba equation, essential for the practical application of this equation.…”

Section: Introductionmentioning

confidence: 99%

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A novel approach for modeling and tracking control of a passive-wheel snake robot

Huang

Shao

Zhen

et al. 2017

Advances in Mechanical Engineering

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This article proposed a novel approach for the dynamic modeling and controller design of a passive-wheel snake robot based on Udwadia-Kalaba theory. Compared to common methods, this approach is easily processed for many-degreeof-freedom snake robot. The desired trajectory is easily modeled as a trajectory constraint, and the nonholonomic constraints from the passive wheels' lateral velocity are also easily handled using Udwadia-Kalaba theory. Besides the proposed equation of motion is analytical, no approximation or linearization as well as extra variables such as Lagrangian multiplier is needed as common methods usually do. The servo joint constraint forces are precisely calculated by solving Udwadia-Kalaba equation, and no complicated control structure design is needed as common control methods always do especially for under-actuated mechanical systems. This article provides a novel dynamic modeling and controller design approach for the passive-wheel snake robot in a new perspective. The theoretical analysis and simulation verify the proposed approach. The trajectory has good incidence with the designed one, and the real-time joint forces are also conveniently acquired.

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Section: Dynamics Of the Snakementioning

confidence: 99%

Section: Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel approach for modeling and tracking control of a passive-wheel snake robot

Huang

Shao

Zhen

et al. 2017

Advances in Mechanical Engineering

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“…The purpose of Assumption 1 is to ensure the desired trajectory reachable. In this paper, to track the desired attitude trajectories accurately, first of all, we need to determine the corresponding constraint in first order (4.2), then by differentiating it with respect to time once again, the second order constraint (4.7) is derived and will be employed to construct a legitimate Lyapunov function for the stabilization and trajectory tracking control problems [27,28].…”

Section: Remarkmentioning

confidence: 99%

A Novel Trajectory Tracking Control Strategy for Underactuated Quadrotor UAV with Uncertainties and Disturbances

Han¹,

Yang²,

Xia³

et al. 2020

Preprint

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In this research, a novel position trajectory tracking control architecture has been constructed for an underactuated quadrotor unmanned aerial vehicle (UAV) with uncertainties and disturbances. Primarily, we divide the whole dynamic system into an underactuated position subsystem and a fully-actuated attitude subsystem. For the position subsystem, we have transformed it into a fully-actuated system by constructing a virtual PD controller, and this controller can render the position tracking error asymptotically stable. Besides, based on the position controller designed for quadrotor UAV, the desired attitudes, i.e. roll, pitch and yaw angles, will be derived. Next, as for the attitude subsystem which is sensitive to uncertainties and external disturbances, a novel robust attitude constraint-following controller is proposed for this aircraft, this attitude controller can not only guarantee the uniform boundedness and uniform ultimate boundedness of constraint deviation, but also does not requiring more information of uncertainties and disturbances except their bounds. Eventually, the simulations have demonstrated a sound tracking performance of our proposed control strategy for quadrotor UAV even in the presence of uncertainties and disturbances.

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“…Many researchers have since used Udwadia-Kalaba's method to solve problems in the dynamics analysis of multibody systems. [15][16][17][18][19][20][21][22][23] Schutte and Dooley 11 utilized the Udwadia-Kalaba approach to study the periodicity of tethered satellite motion. Huang et al used the Udwadia-Kalaba formulation to obtain the closed-form equation of the motion of a human body with joint friction.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis and tracking trajectory control of a crane

Huang

Shunqiang

Zhen

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part E:

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This paper introduces a method to solve the crane motion trajectory control problem. A dynamic model is proposed based on the Udwadia-Kalaba equation, which can be solved without extra parameters, such as the Lagrange multiplier. The motion trajectory of a crane is used as a constraint (referred to as trajectory tracking constraint). To satisfy the system trajectory, a method to calculate the driving conditions on the basis of the above conditions is proposed. A 2D plane dynamic model of a crane is established. Five stages of crane movement are obtained. Simulation is performed with Matlab. Simulation results simulation show that the Udwadia-Kalaba equation can be well applied to trajectory tracking control of cranes.

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Equations of motion of constrained mechanical systems: given force depends on constraint force

Cited by 23 publications

References 4 publications

A novel approach for modeling and tracking control of a passive-wheel snake robot

A novel approach for modeling and tracking control of a passive-wheel snake robot

A Novel Trajectory Tracking Control Strategy for Underactuated Quadrotor UAV with Uncertainties and Disturbances

Dynamic analysis and tracking trajectory control of a crane

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