Control Of Rigid Body Motion Research Articles

Simultaneous Independent Translational and Rotational Feedback Motion Control System for a Cylindrical Magnet using Planar Arrays of Magnetic Sensors and Cylindrical Coils.

This letter describes an electromagnetic feedback control system for rigid-body motion control of a magnet. Its novel features are that sensing and actuation using magnetometer sensors and actuator coils operate simultaneously, and magnetic field models from the controlled magnet and each of the actuator coil currents are used together to calculate the 3D position and orientation of the magnet to control motion simultaneously and independently in multiple degrees of freedom including planar translation and two in rotation, leaving rotation about the cylindrical axis of magnetization uncontrolled. The system configuration and the localization and actuation methods are presented with experimental results of magnet localization with constant and varying coil currents, and during feedback control of trajectory following motion of the magnet in multiple directions on a planar surface and with controlled changes in orientation. The intended application of the system is for motion control of magnetic endoscope capsules and other miniature medical devices inside the human body.

Pose Control for Rigid Body Motion with an Input-to-state Safe Control Barrier Function

In this paper, we present a pose control method for rigid body motion via an input-to-state safe control barrier function (ISSf-CBF). After discussing the kinematic model for a rigid body, we design an ISSf-CBF for obstacle avoidance. Next, we present a control Lyapunov function (CLF) for a control error system which possesses a passivity property. By using the ISSf-CBF and CLF, we discuss a unified quadratic program formulation that ensures both safety and stability for pose control of rigid body motion under input disturbances. Our proposed approach, which deals with both the position and the orientation of rigid body motion, connects the safety and the stability via the ISSf-CBF and the CLF under input disturbances. Finally, simulation results confirm the validity of the proposed ISSf-CBF control method compared to the stabilizing one.

Disturbance Rejection by Acceleration Feedforward for Marine Surface Vessels

Acceleration signals have a powerful disturbance rejection potential in rigid body motion control, as they carry a measure proportional to the resulting force. Yet, they are seldom used, since measuring, decoupling, and utilizing the dynamic acceleration in the control design is not trivial. This paper discusses these topics and presents a solution for marine vessels building on conventional methods together with a novel control law design, where the dynamic acceleration signals are used to form a dynamic referenceless disturbance feedforward compensation. This replaces conventional integral action and enables unmeasured external loads and unmodel dynamics to be counteracted with low time lag. A case study shows the feasibility of the proposed design using experimental data and closed-loop high fidelity simulations of dynamic positioning in a harsh cold climate environment with sea-ice.

Optimal LQ feedforward tracking with preview: Practical design for rigid body motion control

For reference-tracking motion control, preview-based linear quadratic (LQ) design methods provide an effective means to balance tracking performance with available actuation capacity. This paper considers a control structure for which the optimal feedforward controller is independent of the feedback controller. In this way, explicit implementation formulas for feedforward controllers are derived that can be applied to a range of rigid-body motion systems. Key aspects of the optimal LQ solutions are identified, particularly how the choice of design weightings affect steady-state error for polynomial tracking. A redesign procedure for finite preview-time is proposed that preserves exact polynomial tracking properties and control bandwidth of the optimal solutions. Comparative experimental results are presented for a motor-driven linear motion stage.

Optimal coordination and control of posture and movements

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton–Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

Hybrid Input Shaping and Feedback Control Schemes of a Flexible Robot Manipulator

This paper presents investigations into the development of hybrid control schemes for input tracking and vibration control of a flexible robot manipulator. A constrained planar single-link flexible manipulator is considered and the dynamic model of the system is derived using the assume mode method. To study the effectiveness of the controllers, initially a collocated PD control is developed for control of rigid body motion. This is then extended to incorporate input shaper control schemes for vibration control of the system. The positive and modified specified negative amplitude input shapers are designed based on the properties of the system. Simulation results of the response of the manipulator with the controllers are presented in time and frequency domains. The performances of the hybrid control schemes are examined in terms of level of input tracking capability, vibration reduction, time response specifications and robustness to parameters uncertainty in comparison to the PD control. Finally, a comparative assessment of the amplitude polarities of the input shapers to the system performance is presented and discussed.

Hybrid Learning Control Schemes with Acceleration Feedback of a Flexible Manipulator System

This paper presents investigations into developing a hybrid iterative learning control scheme with acceleration feedback. An experimental flexible manipulator rig and corresponding simulation environment are used to demonstrate the effectiveness of the proposed control strategy. A collocated proportional-derivative controller utilizing hub-angle and hub-velocity feedback is developed for control of rigid-body motion of the system. This is then extended to incorporate iterative learning control with acceleration feedback and genetic algorithms for optimization of the learning parameters for control of vibration (flexible motion) of the system. The system performance with the controllers is presented and analysed in the time and frequency domains. The performance of the hybrid learning control scheme without and with acceleration feedback is assessed in terms of input tracking and level of vibration reduction at resonance modes and robustness to variation in payload.

Hybrid learning control schemes with input shaping of a flexible manipulator system

The paper describes a practical approach to investigate and develop a hybrid iterative learning control scheme with input shaping. An experimental flexible manipulator rig and corresponding simulation environment are used to demonstrate the effectiveness of the proposed control strategy. A collocated proportional-derivative (PD) controller utilizing hub-angle and hub-velocity feedback is developed for control of rigid-body motion of the system. This is then extended to incorporate iterative learning control with acceleration feedback and genetic algorithms (GAs) for optimization of the learning parameters and a feedforward controller based on input shaping techniques for control of vibration (flexible motion) of the system. The system performance with the controllers is presented and analysed in the time and frequency domains. The performance of the hybrid learning control scheme with input shaping is assessed in terms of input tracking and level of vibration reduction. The effectiveness of the control schemes in handling various payloads is also studied.

Optimal control of rigid body motion with the help of rotors using stereographic coordinates

Abstract This paper considers the problem of optimal controlling the rotational motion of a rigid body using three independent control torques developed by three rotors attached with the principal axes of inertia of the body and rotate with the help of electric motors rigidly mounted on the body. The optimal control law is given as non-linear function of new parameterizations of the rotation group derived by using the stereographic projection of the Euler parameters. Given a cost function we seek for a stabilizing feedback control law that minimizes this cost and asymptotically stabilizes the rotational motion of the body. The stabilizing properties of the proposed controllers are proved by using the optimal Liapunov function. Numerical examples and simulation study are presented.

Vibration control of a very flexible manipulator system

This paper presents experimental investigations into the development of feedforward and feedback control schemes for vibration control of a very flexible and high-friction manipulator system. A feedforward control scheme based on input shaping and low-pass filtering techniques and a strain feedback control scheme are examined. To study the effectiveness of the controllers, initially a collocated PD control is developed for control of rigid body motion. The performances of the controllers are assessed in terms of the input tracking capability and vibration reduction as compared to the response with PD control. Moreover, the robustness of the feedforward control schemes is discussed. Finally, a comparative assessment of the control strategies is presented.

Hybrid control schemes for input tracking and vibration suppression of a flexible manipulator

This paper presents investigations into the development of hybrid control schemes for input tracking and end-point vibration suppression of a flexible manipulator system. The dynamic model of the flexible manipulator is derived using the finite element method. Initially, a collocated proportional-derivative (PD) controller utilizing hub angle and hub velocity feedback is developed for control of rigid-body motion of the system. This is then extended to incorporate a non-collocated proportional-integral-derivative (PID) controller and a feedforward controller based on input shaping techniques for control of vibration (flexible motion) of the system. Simulation results of the response of the manipulator with the controllers are presented in time and frequency domains. The performances of the hybrid control schemes are assessed in terms of input tracking and level of vibration reduction in comparison to the PD control. The effectiveness of the control schemes in handling various payloads is also studied. Finally, a comparative assessment of the hybrid control schemes is presented.

Hybrid control schemes for input tracking and vibration suppression of a flexible manipulator

This paper presents investigations into the development of hybrid control schemes for input tracking and end-point vibration suppression of a flexible manipulator system. The dynamic model of the flexible manipulator is derived using the finite element method. Initially, a collocated proportional-derivative (PD) controller utilizing hub angle and hub velocity feedback is developed for control of rigid-body motion of the system. This is then extended to incorporate a non-collocated proportional-integral-derivative (PID) controller and a feedforward controller based on input shaping techniques for control of vibration (flexible motion) of the system. Simulation results of the response of the manipulator with the controllers are presented in time and frequency domains. The performances of the hybrid control schemes are assessed in terms of input tracking and level of vibration reduction in comparison to the PD control. The effectiveness of the control schemes in handling various payloads is also studied. Finally, a comparative assessment of the hybrid control schemes is presented.

Simultaneous rigid-body motion and vibration control of a flexible four-bar linkage

A model and a control scheme for a flexible four-bar linkage is described. The discrete finite element model of the mechanism accounts for geometric and inertial nonlinearities. A reduced number of measured variables are selected to control both rigid-body motion and vibration separately. Rigid-body motion control is performed by means of a PID-like regulator while proportional controllers are employed to damp link oscillations. Appropriate devices are proposed to avoid coupling effects among variables. Numerical results demonstrate the effectiveness of the control scheme.

Suboptimal control of rigid body motion with a quadratic cost

In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.

Vibration Control Experiment of a Slewing Flexible Beam

Two high-authority control/low-authority control algorithms are presented and experimentally validated on a fast slewing beam system. The first one termed the constrained motion method in two-stage (CMM-TS) accomplishes the rigid-body motion control and the optimal control of vibration suppression by a stepping motor. Another termed the constrained motion method in combination (CMM-CO) combines both the optimal control from stepping motor and active damping control from piezoelectric actuator for vibration suppression. Experimental results show that these algorithms are concise in formulation, efficient in hardware realization, and effective in vibration suppression.

Suboptimal Control of Rigid Body Motion with a Quadratic Cost

This paper considers the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set satisfy a specified bound on a quadratic performance index or cost. For a special class of cost functions, we present explicit expressions for the optimal stabilizing controllers. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.

Optimal coordination and control of posture and locomotion

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and stance model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses.

Active Vibration Control of Three-Dimensional Flexible Frame Structure. Continued Report, Extension to the Case of Time-Varying Shape and Attitude.

A modal analysis is presented, by which the dynamics of time-varying frame structures under RD-control can be predicted with high accuracy, within short computation time and without causing the observation or control spillover at all. As numerical examples, deploying or rotatiog space structures and a moving arm are used. It is shown that the modal analysis presented here can be applied to the control of rigid-body motion of the space structures, which cannot be controlled by DVFB. for the rotating space structures and the moving arm, influencies of the reaction force and torque respectively due to the time-varying momentum and angular momentum of the rotating member beams on the controlled responses are studied.

Quadratic optimization of motion coordination and control

Algorithms for continuous-time quadratic optimization of motion control are presented. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are found by solving an algebraic matrix equation. The system stability is investigated according to Lyapunov function theory and it is shown that global asymptotic stability holds. How optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters is shown. The solution results in natural design parameters in the form of square weighting matrices, as known from linear quadratic optimal control. The proposed optimal control is useful both for motion control, trajectory planning, and motion analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Active suspension control for the flexible structure of an elastic vehicle body. (Theoretical analysis for control of rigid body motion and elastic vibration).

From a viewpoint of energy saving, it is required to design a lightweight vehicle body for high speed ground vehicles, but disadvantages will occur such as bending vibration of flexible structures and uncomfortable ride quality. It is proposed to design control systems of flexible vehicle body with two suspensions, by multi-variable control methods of centralized control and decentralized control. By frequency analysis and spectral analysis, it is found that the ride quality and stability of the flexible vehicle system is clearly improved by the actively controlled suspension proposed in this paper.