Identification and Control of Multidimensional Delayed Processes in Conditions of Incomplete Information

Problems of identification and control of multidimensional discrete-continuous processes with delay in conditions of incomplete information about the object are considered. In such conditions, the form of parametric equations for various channels of the object is absent due to the lack of a priori information. Moreover, multidimensional processes have stochastic dependences of the components of the vector of output variables. Under such conditions, the mathematical description of such processes leads to a system of implicit equations. Nonparametric identification and control algorithms for multidimensional systems are proposed. The main task of modeling such processes is to determine the predicted values of the output variables from the known input. Moreover, for implicit equations, it is only known that one or another output variable can depend on other input and output variables that determine the state of a multidimensional system. In this study, a nontrivial situation arises when solving a system of implicit equations under conditions when the dependences between the components of the output variables are unknown. The application of the parametric theory of identification in this case will not lead to success. One of the possible directions is the use of the theory of nonparametric systems. The main content of the work is the solution of the identification problem in the presence of dependencies of the output variables and then the solution of the control problem for such a process. Here you should pay attention to the fact that when determining the reference actions for a multidimensional system, it is first necessary to solve the system of reference actions, since it is not possible to choose arbitrarily setting influences from the range of definition of output variables. Computational eXperiments aimed at investigating the effectiveness of the proposed identification and control algorithms are presented.

Dry Friction and Mechanical System Motion Implicit Equations

It is shown that forces acting on the mechanical system points could depend on accelerations of the system points. Differential equation system of the mechanical system motion appears to be implicit. It is not resolved with respect to senior derivatives. Fundamental mathematical problems appear associated with possibility and uniqueness of these equations' solution with respect to the senior derivatives. Such problems are common in mechanical systems with dry sliding friction and rolling friction. Such problems are missing in the point dynamics. However, such problems are rather typical in more complex mechanical systems appearing in the study of a rigid body motion, which entire mass is concentrated in a single point, as well as in systems with one degree of freedom. Four fairly simple examples of mechanical systems are considered, and their motion is described by implicit differential motion equations. Situations could appear in these systems, when motion equations are not solvable with respect to the senior derivatives (motion equations are missing), as well as situations, when there are several solutions with respect to senior derivatives (there are several different systems of the mechanical system motion equations). At the same time, one of the fundamental principles of mechanics is not fulfilled, i.e., the principle of determinism

Vision-based kinematic analysis of the Delta robot for object catching

SUMMARY This paper proposes a vision-based kinematic analysis and kinematic parameters identification of the proposed architecture, designed to perform the object catching in the real-time scenario. For performing the inverse kinematics, precise estimation of the link lengths and other parameters needs to be present. Kinematic identification of Delta based upon Model10 implicit model with ten parameters using the iterative least square method is implemented. The loop closure implicit equations have been modelled. In this paper, a vision-based kinematic analysis of the Delta robots to do the catching is discussed. A predefined library of ArUco is used to get a unique solution of the kinematics of the moving platform with respect to the fixed base. The re-projection error while doing the calibration in the vision sensor module is 0.10 pixels. Proposed architecture interfaced with the hardware using the PID controller. Encoders are quadrature and have a resolution of 0.15 degrees embedded in the experimental setup to make the system closed-loop (acting as feedback unit).

Recursive Gauss-Helmert model with equality constraints applied to the efficient system calibration of a 3D laser scanner

Sensors for environmental perception are nowadays applied in numerous vehicles and are expected to be used in even higher quantities for future autonomous driving. This leads to an increasing amount of observation data that must be processed reliably and accurately very quickly. For this purpose, recursive approaches are particularly suitable in terms of their efficiency when powerful CPUs and GPUs are uneconomical, too large, or too heavy for certain applications. If explicit functional relationships between the available observations and the requested parameters are used to process and adjust the observation data, complementary approaches exist. The situation is different for implicit relationships, which could not be considered recursively for a long time but only in the context of batch adjustments. In this contribution, a recursive Gauss-Helmert model is presented that can handle explicit and implicit equations and thus allows high flexibility. This recursive estimator is based on a Kalman filter for implicit measurement equations, which has already been used for georeferencing kinematic multi-sensor systems (MSS) in urban environments. Furthermore, different methods for introducing additional information using constraints and the resulting added value are shown. Practical application of the methodology is given by an example for the calibration of a laser scanner for a MSS.

An implicit constitutive relation for describing the small strain response of porous elastic solids whose material moduli are dependent on the density

In this short note, we develop a constitutive relation that is linear in both the Cauchy stress and the linearized strain, by linearizing implicit constitutive relations between the stress and the deformation gradient that have been put into place to describe the response of elastic bodies (Rajagopal, KR. On implicit constitutive theories. Applications of Mathematics 2003; 28: 279–319), by assuming that the displacement gradient is small. These implicit equations include the classical linearized elastic constitutive approximation as well as some classes of constitutive relations that imply limiting strain in tension, as special subclasses. Moreover, the constitutive relations that are developed allow the material moduli to depend on the density; thus, they can be used to describe the response of porous materials, such as porous metals, bone, rocks, and concrete undergoing small deformations.

Implicit Equations Involving the p-Laplace Operator

In this work we study the existence of solutions $$u \in W^{1,p}_0(\Omega )$$ u ∈ W 0 1 , p ( Ω ) to the implicit elliptic problem $$ f(x, u, \nabla u, \Delta _p u)= 0$$ f ( x , u , ∇ u , Δ p u ) = 0 in $$ \Omega $$ Ω , where $$ \Omega $$ Ω is a bounded domain in $$ {\mathbb {R}}^N $$ R N , $$ N \ge 2 $$ N ≥ 2 , with smooth boundary $$ \partial \Omega $$ ∂ Ω , $$ 1< p< \infty $$ 1 < p < ∞ , and $$ f:\Omega \times {\mathbb {R}}\times {\mathbb {R}}^N \times {\mathbb {R}}\rightarrow {\mathbb {R}}$$ f : Ω × R × R N × R → R . We choose the particular case when the function f can be expressed in the form $$ f(x, z, w, y)= \varphi (x, z, w)- \psi (y) $$ f ( x , z , w , y ) = φ ( x , z , w ) - ψ ( y ) , where the function $$ \psi $$ ψ depends only on the p-Laplacian $$ \Delta _p u $$ Δ p u . We also present some applications of our results.

Numerical Design Method for CVT Supported in Standard Variable Speed Rubber V-Belts

The design of a V-belt continuously variable transmission (CVT) system is a complex problem due to the multiple interactions between components during its operation. Literature on CVT system design methods is scarce, and the vast majority of works include implicit equations that hinder applications at a basic design level. This research aims to introduce a numerical CVT design method for electric vehicles (EV) and internal combustion engine (ICE) vehicles considering each one of their components and using mechanical centrifugal actuators and a rubber V-belt. This design method is based on user needs, for which there are three main requirements: road specifications, vehicle characteristics, and expected performance. This method is focused on a transmission for a vehicle traveling on the same route constantly, such as public transport vehicles. From three-wheelers to medium cargo vehicles, there is a greatly diverse range of potential applications for using this method for each type of standard rubber V-belt.

Underwater 3D Doppler-Angle Target Tracking with Signal Time Delay

The traditional target tracking is a process of estimating the state of a moving target using measurement information obtained by sensors. However, underwater passive acoustic target tracking will confront further challenges, among which the system incomplete observability and time delay caused by the signal propagation create a great impact on tracking performance. Passive acoustic sensors cannot accurately obtain the target range information. The introduction of Doppler frequency measurement can improve the system observability performance; signal time delay cannot be ignored in underwater environments. It varies with time, which has a continuous negative impact on the tracking accuracy. In this paper, the Gauss–Helmert model is introduced to solve this problem by expanding the unknown signal emission time as an unknown variable to the state. This model allows the existence of the previous state and current state at the same time, while handling the implicit equations. To improve the algorithm accuracy, this paper further takes advantage of the estimated state and covariance for the second stage iteration and propose the Gauss–Helmert iterated Unscented Kalman filter under a three-dimensional environment. The simulation shows that the proposed method in this paper shows superior estimation accuracy and more stable performance compared with other filtering algorithms in underwater environments.