Rigid Body Dynamics

From, Pål Johan; Gravdahl, Jan Tommy; Pettersen, Kristin Y.

doi:10.1007/978-1-4471-5463-1_6

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…The central points of the three positioning balls were called points A, B, and C, assuming that the three points were located on the x-y plane. The infinitesimal rotation angle of a rigid body is a vector and can be calculated by using the vector operation rule [18]. The rotation of the optical unit around the x-axis and y-axis can be decomposed into rotations of the three points around the line of the other two points respectively.…”

Section: Mathematical Model Of Rotation Anglesmentioning

confidence: 99%

Design of Positioning Mechanism Fit Clearances Based on On-Orbit Re-Orientation Accuracy

Yang

Zhao

et al. 2019

Applied Sciences

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The factors affecting the re-orientation accuracy of the on-orbit replaceable optical unit were studied, and the mathematical models of the relationships between fit clearances of positioning mechanisms and the limits of rotation angles were deduced. When the relative position relationship of positioning mechanisms was determined, fit clearances were designed according to the requirement of the rotation angle limits, and the rotation angle limits were determined to ensure that the angles were within the index range. Theodolites were used to measure the re-orientation angles of the optical unit, and the errors between the measurement angles and the real angles were deduced. Then, the numerical simulation proved that the errors were within limits. The microgravity test environment was established, and the weight of the optical unit was unloaded by a suspension method to simulate the state of the optical unit when it was replaced on orbit. The test results confirmed the correctness of the design method.

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Section: Mathematical Model Of Rotation Anglesmentioning

confidence: 99%

Design of Positioning Mechanism Fit Clearances Based on On-Orbit Re-Orientation Accuracy

Yang

Zhao

et al. 2019

Applied Sciences

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“…where L represents the Lagrangian function (the Lagrangian), K is the kinetic energy, U is the potential energy, q is the vector of generalized coordinates (joints), q is the generalized velocity vector (of the joints), and τ is the generalized forces vector (forces and torques). In this way, the dynamic model of a manipulator of n joints can be expressed by means of (14) [19][20][21][22],…”

Section: Dynamicsmentioning

confidence: 99%

Trajectory Tracking Control of a Real Redundant Manipulator of the SCARA Type

Urrea¹,

Kern²

2016

Journal of Electrical Engineering and Technology

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-Modeling, control and implementation of a real redundant robot with five Degrees Freedom (DOF) of the SCARA (Selective Compliant Assembly Robot Arm) manipulator type is presented. Through geometric methods and structural and functional considerations, the inverse kinematics for redundant robot can be obtained. By means of a modification of the classical sliding mode control law through a hyperbolic function, we get a new algorithm which enables reducing the chattering effect of the real actuators, which together with the learning and adaptive controllers, is applied to the model and to the real robot. A simulation environment including the actuator dynamics is elaborated. A 5 DOF robot, a communication interface and a signal conditioning circuit are designed and implemented for feedback. Three control laws are executed in: a simulation structure (together with the dynamic model of the SCARA type redundant manipulator and the actuator dynamics) and a real redundant manipulator of the SCARA type carried out using MatLab/Simulink programming tools. The results, obtained through simulation and implementation, were represented by comparative curves and RMS indices of the joint errors, and they showed that the redundant manipulator, both in the simulation and the implementation, followed the test trajectory with less pronounced maximum errors using the adaptive controller than the other controllers, with more homogeneous motions of the manipulator.

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Efficient AoA-Based Rigid Body Localization via Single Base Station for Internet of Things Applications

et al. 2019

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For many data mining applications under the Internet of Things (IoT) environments, the attitude and the position of a rigid target are indispensable and hidden information to be dug. The term Rigid Body Localization (RBL) refers to simultaneously estimation of the position and the attitude of a rigid target. The RBL framework which adopts only one single base station (BS) is considered in this paper for IoT applications. Several wireless sensor nodes with known topology information are fixed on the surface of the rigid target. The single BS fuses the angle of arrival (AoA) measurements from the nodes with the topology information for the RBL purpose. In this paper, we propose a two-stage RBL method to efficiently fusing the aforementioned two pieces of information. Firstly, we built the maximum likelihood estimator (MLE) of the information fusion and adopted the modified Newton's iteration algorithm (mNIA) to determine the wireless node position; then we used the unit quaternion (UQ) algorithm for estimating the relative position and attitude with respect to the predetermined reference state, which completed the RBL task. Finally, we evaluated the proposed RBL performance in terms of the root mean squared error (RMSE), convergence success rate, as well as the computation costs. Simulation results showe that the proposed mNIA-based RBL algorithm can achieve a finer RBL performance with obviously higher speed and 100 percent success convergence rate, comparing with existing heuristic methods. INDEX TERMS Internet of Things, heuristic algorithms, computational cost, rigid body localization, angle of arrival.

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Rigid Body Dynamics

Cited by 3 publications

References 20 publications

Design of Positioning Mechanism Fit Clearances Based on On-Orbit Re-Orientation Accuracy

Design of Positioning Mechanism Fit Clearances Based on On-Orbit Re-Orientation Accuracy

Trajectory Tracking Control of a Real Redundant Manipulator of the SCARA Type

Efficient AoA-Based Rigid Body Localization via Single Base Station for Internet of Things Applications

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