Computing a Manipulator Regressor Without Acceleration Feedback

S INCE some catastrophic faults or failures may be induced due to the aging or damage of actuators and sensors during the mission of a spacecraft, those faults would lead to performance degradation of the spacecraft attitude control system or even result in the specified aerospacemission failure. Therefore, fault tolerance of the spacecraft attitude control system is one of the key issues that needs to be addressed. With a view to tackle such a challenge, fault-tolerant control (FTC) has received considerable attention in order to enhance the spacecraft reliability and to guarantee the attitude control performance [1–5]. In [5], an adaptive FTC is developed for the flexible spacecraft attitude tracking system where the persistent bounded disturbances, unknown inertia parameter, and even two types of reaction wheel faults are successfully accommodated. Indeed, the aforementioned approaches offer many attractive conceptual features, but at the same time they are derived based on the availability of direct and exact measurements of both the angular velocity and the attitude orientation. It is important to note, however, that when it comes to practical implementation, the angular velocity measurements are not always available because of either cost limitations or implementation constraints. Motivated from such a practical consideration, it is therefore highly desirable to develop partial state feedback attitude control strategies with spacecraft angular velocity measurements eliminated. The issue has been addressed in the literature by using observer-based control [6,7], Lyapunov-based control [8,9], and variable structure control [10] under normal operation of spacecraft. In this work, we provide solutions to two different problems of the flexible spacecraft attitude control system. The first problem consists of developing a control law to perform a attitude stabilization maneuver without angular velocity magnitude. In contrast with the velocity-free control schemes available in the literature, the presented approach can guarantee the attitude control performance be greatly robust to external disturbances and unknown inertia parameters. The second problem solved is the casewhere both loss of control effectiveness and additive fault occur in actuators simultaneously, but the attitude still requires stabilization with high resolution. To the best knowledge of the authors, this study is the first attempt to deal with fault-tolerant attitude stabilization control for flexible spacecraft with the angular velocity magnitude eliminated. The Note is organized as follows. Section II presents the mathematical model and attitude control problems formation of a flexible spacecraft under normal and faulty actuator conditions. Section III presents the proposed fault-tolerant attitude stabilization controller without velocity magnitude in the presence of two types of actuator faults. Simulation results to demonstrate various features of the proposed scheme are given in Sec. IV followed by conclusions in Sec. V.

Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an n -dimensional convex body within multiplicative error ε using Õ(n 3 + n 2.5 /ε ) queries to a membership oracle and Õ(n 5 +n 4.5 /ε) additional arithmetic operations. For comparison, the best known classical algorithm uses Õ(n 3.5 +n 3 /ε 2 ) queries and Õ(n 5.5 +n 5 /ε 2 ) additional arithmetic operations. To the best of our knowledge, this is the first quantum speedup for volume estimation. Our algorithm is based on a refined framework for speeding up simulated annealing algorithms that might be of independent interest. This framework applies in the setting of “Chebyshev cooling,” where the solution is expressed as a telescoping product of ratios, each having bounded variance. We develop several novel techniques when implementing our framework, including a theory of continuous-space quantum walks with rigorous bounds on discretization error. To complement our quantum algorithms, we also prove that volume estimation requires Ω (√ n+1/ε) quantum membership queries, which rules out the possibility of exponential quantum speedup in n and shows optimality of our algorithm in 1/ε up to poly-logarithmic factors.

A new probability distribution evolution algorithm (PDE) is proposed for inertial parameters identification of space target. Based on the conservation of angular momentum, the number of space target's inertial unknown parameters is reduced from 10 to 4 by using pseudo inverse operation. The pseudo-inverse solution consistency in multiple groups status is proposed as the optimization evaluation index, and identification simulations are carried out using PDE. A evaluation strategy is given to significantly improve identification accuracy while a small increase of calculation consumption. The statistical results of identification simulation examples show that by only using angular momentum measurement data, the proposed PDE and strategy can achieve the high precision identification for the target inertial parameters with large range change. And PDE is equivalent to the optimization ability of typical evolutionary algorithms, such as genetic algorithm (GE) and differential evolution algorithm (DE).

Quasi-exponential Stabilization of Wheeled Mobile Robots with Uncertainty

A projection scheme to handle eigenvalue bounds for adaptive control with uncertain symmetric matrix parameters is introduced. Conventional parameter projection techniques are generally unable to handle explicit eigenvalue bounds. The continuous projection scheme presented here maintains the closed-loop stability properties for adaptive controllers while simultaneously satisfying <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> available eigenvalue bounds of the uncertain symmetric matrix valued parameters. The projection scheme uses the eigen decomposition of the symmetric matrix parameter to project its eigenvalues to lie within the prescribed bounds. The eigenvalues of the symmetric matrix may be lower bounded or upper bounded or both. A direct adaptation over the eigenvalues and the eigen projections of the symmetric matrix parameter is also derived to help circumvent expensive eigen decomposition calculations. The new projection here shows improved performance in numerical simulations of rigid body attitude tracking control and trajectory tracking of robotic manipulators with unknown inertia parameters.

Considers the tracking problem of dynamic nonholonomic systems with unknown inertia parameters. A new controller is proposed. The proposed controller not only ensures the entire state of the dynamic system asymptotically track the desired trajectory, but also is characterized by low dimension and the absence of singular points. Simulation results show that the proposed controller is effective.

A novel viscoelastic model of four-wire suspension structure with damping gel in an optical pickup actuator was identified and validated. A two-stage method was developed for the identification of inertia, damping, and spring parameters in the dynamic model. The inertia and spring parameters were identified from static tests. With the identified parameters in the dynamic model, the damping parameters were identified through sinusoidal excitation tests. The accuracy of utilizing fractional derivative to model the damping of polymer damper was validated by carrying out error analysis. The fractional transfer function with voltage input was identified and compared with the transfer function of classical model.

&lt;p&gt;Due to their advantage of high speed, accuracy and repeatability, robot manipulators have become major component of manufacturing industries and even now a days they become part of routine life. &lt;/p&gt;&lt;p&gt;Two link robot manipulator is a very basic classical and simple example of robot followed in understanding of basic fundamentals of robotic manipulator. The equation of motion for two link robot is a nonlinear differential equation. For higher degrees of freedom, as the closed form solutions are very difficult we have to use numerical solution. Here we focused mainly on control of robot manipulator to get the desired position using combination of two classical methods PID and computed torque control method after deriving the equation of motion. For the same simulation is represented using MATLAB and compared with computed torque control method.&lt;/p&gt;

Event-triggered adaptive control for attitude tracking of spacecraft

In this article we formulate, in a Lie group setting, the equations of motion for a system of n coupled rigid bodies subject to holonomic constraints. A mapping $f: { \cal {M} \rightarrow \cal {N}$ is constructed, where $\cal M$ is the m-dimensional configuration manifold of the system, and $\cal{N} = \rm{SE(3)} \times \cdots \times \rm{SE(3)}$ (n copies) is endowed with the left-invariant Riemannian metric h corresponding to the total kinetic energy of the system, where SE(3) is the special Euclidean group. The generalized inertia tensor of the system is given by the pullback metric $f^*h$ ; the equations of motion are then the geodesic equations on $\cal M$ with respect to this metric. We show how this coordinate-free formulation leads directly to a factorization of the generalized inertia tensor of the form ${\cal S}^T {\cal L}^T {\cal H} {\cal L} {\cal S}$ , where $\cal S$ is a constant block-diagonal matrix consisting only of kinematic parameters, $\Cal H$ is a constant block-diagonal matrix consisting only of inertial parameters, and ${\cal L}$ is a block lower-triangular matrix composed of Adjoint operators on se(3). Such a factorization is useful for various multibody system dynamics applications, e.g., inertial parameter identification, adaptive control, and design optimization. We also show how in many practical situations ${\cal N}$ can be reduced to a submanifold, thereby considerably simplifying the derivation of the equations of motion. Our geometric formulation not only suggests ways to choose the best coordinates for analysis and computation, but also provides high-level insight into the structure of the equations of motion.

In this paper, we present a real-time method for identification of the inertial parameters of a humanoid robot and an estimation of its center-of-mass (CoM)and linear and angular momentum. CoM and momentum are important for whole-body motion generation of a humanoid robot and can be used as an indicator of motion planning. Because they are affected by modeling errors and inertia changes (e.g., due to object grasping), it is important to estimate them online. The proposed method has the advantage of being based only on the internal sensors. We verified the effectiveness of the proposal method by applying it to a humanoid robot.

This paper investigates the stabilization problem of uncertain dynamic non-holonomic chained systems with unknown constant inertia parameters. Globally time-varying adaptive stabilizing control laws for such systems are presented. The application of it to a non-holonomic wheeled mobile robot is described. Simulation results show that the proposed approach is effective.

Nonsynchronous perturbation techniques developed over the last few years have proven to be a very powerful tool for parameter identification of rotating systems. In order to obtain interpretable results, some limitations have had to be imposed on the analytical models and rotor systems used in the process, such as applied forces, and measurement transducers had to be located near major masses on the rotor. In the laboratory environment these limitations can usually be accommodated, but not always, while in the field, compliance is almost impossible. This paper explores the use of finite element modeling, measured vibration response data, and optimization techniques to extend the applicability of parameter identification through nonsynchronous perturbation techniques to those systems in which the perturbation forces and/or resultant response measurements cannot be conveniently located at the mass centers. In this technique, a finite element model of the rotor system is constructed, and all known information about the system parameters input to a computer program designed to operate on a personal computer. The program then computes the theoretical response of the system, by processing user-supplied initial conditions for the unknown system parameters, and compares these results with the vibration responses measured on the machine, and collected by the data acquisition system. The unknown parameters are then modified using local convergence optimization techniques until the error between the theoretical and measured responses is acceptably small. If the system parameters under investigation coincide with the unknown parameters in the computer program, they are identified in the process. This technique was applied to an experimental rotor system constructed such that the parameters under investigation, the direct and quadrature dynamic stiffness components for a plain oil-lubricated journal bearing operating at low eccentricity, could be determined by both this technique and conventional unbalance force testing. The results of the nonsynchronous tests are presented in the paper.

This letter highlights some issues which were overlooked in a recently published paper called maximum likelihood identification of inertial sensor noise model parameters. The latter paper does not consider existing alternative methods, which specifically tackle this issue in a possibly more direct manner and, although remaining a generally valid proposal, does not appear to improve on the earlier proposals. Finally, a simulation study rectifies the poor results of an estimator of reference in the same publication.

We develop efficient kernels for elemental operators of matrix-free solvers of the Helmholtz equation, which are the core operations for incompressible Navier-Stokes solvers, for use on graphics-processing units (GPUs). Our primary concern in this work is the extension of matrix-free routines to efficiently evaluate this elliptic operator on regular and curvilinear triangular elements in a tensor-product manner. We investigate two types of efficient CUDA kernels for a range of polynomial orders and thus varying arithmetic intensities: the first maps each elemental operation to a CUDA-thread for a completely vectorised kernel, whilst the second maps each element to a CUDA-block for nested parallelism. Our results show that the first option is beneficial for elements with low polynomial order, whereas the second option is beneficial for elements of higher order. The crossover point between these two schemes for the hardware used in this study corresponds to polynomial orders at around P=4−5, depending on element type. For both options, we highlight the importance of the layout of data structures, which necessitates the development of interleaved elemental data for vectorised kernels, and analyse the effect of selecting different memory spaces on the GPU. As the considered kernels are foremost memory-bandwidth bound, we develop kernels for curved elements that trade memory bandwidth against additional arithmetic operations, and demonstrate improved throughput in selected cases. We further compare our optimised CUDA kernels against optimised OpenACC kernels, to contrast the performance between a native and a portable programming model for GPUs.