arXiv subjects

Farhad Aghili

Publications and source records attributed to Farhad Aghili.

28 records · Page 2Linked to original sources

arXiv2022

Autonomous Driving Vehicles Using Adaptive Learning Method for Data Fusion

This paper presents an adaptive learning method for data fusion in autonomous driving vehicles. The localization is based on the integration of Inertial Measurement Unit (IMU) with two Real-Time Kinematic (RTK) Global Positioning System (GPS) units in an adaptive Kalman filter (KF). The observability analysis reveals that $i$) integration of a single GPS with IMU does not constitute an observable system; $ii$) integration of two GPS units with IMU results in a locally observable system provided that the line connecting two GPS antennas is not parallel with the vector of the measured acceleration, i.e., the sum of inertial and gravitational accelerations. The latter case makes it possible to compensate for the error in the estimated orientation due to gyro drift and its bias without needing additional instruments for absolute orientation measurements, e.g., a magnetic compass. Moreover, in order to cope with the fact that GPS systems sometimes lose their signal and receive inaccurate position data, the self-tuning filter estimates the covariance matrix associated with the GPS measurement noise. This allows the KF to incorporate GPS measurements in the data fusion process heavily only when the information received by GPS becomes reliably available.

eess.SY↗

arXiv2022

Machine Learning for LiDAR-Based Navigation System

This paper presents a robust 6-DOF relative navigation by combining the iterative closet point (ICP) registration algorithm and a noise-adaptive Kalman filter (AKF) in a closed-loop configuration together with measurements from a laser scanner and an inertial measurement unit (IMU). In this approach, the fine-alignment phase of the registration is integrated with the filter innovation step for estimation correction while the filter estimate propagation provides the coarse alignment needed to find the corresponding points at the beginning of ICP iteration cycle. The convergence of the ICP point matching is monitored by a fault-detection logic and the covariance associated with the ICP alignment error is estimated by a recursive algorithm. This ICP enhancement has proven to improve robustness and accuracy of the pose tracking performance and to automatically recover correct alignment whenever the tracking is lost. The Kalman filter estimator is designed so as to identify the required parameters such as IMU biases and location of the spacecraft center-of-mass (CoM).

eess.SY↗

arXiv2022

Optimal Control of Legged-Robots Subject to Friction Cone Constraints

A hierarchical control architecture is presented for energy-efficient control of legged robots subject to variety of linear/nonlinear inequality constraints such as Coulomb friction cones, switching unilateral contacts, actuator saturation limits, and yet minimizing the power losses in the joint actuators. The control formulation can incorporate the nonlinear friction cone constraints into the control without recourse to the common linear approximation of the constraints or introduction of slack variables. A performance metric is introduced that allows trading-off the multiple constraints when otherwise finding an optimal solution is not feasible. Moreover, the projection-based controller does not require the minimal-order dynamics model and hence allows switching contacts that is particularly appealing for legged robots. The fundamental properties of constrained inertia matrix derived are similar to those of general inertia matrix of the system and subsequently these properties are greatly exploited for control design purposes. The problem of task space control with minimum (point-wise) power dissipation subject to all physical constraints is transcribed into a quadratically constrained quadratic programming (QCQP) that can be solved by barrier methods.

eess.SY↗

arXiv2021

Divergent Integrals of Certain Analytical Functions In the Sense of Zeta Regularization

In this paper we extend the Zeta function regularization technique, which gives a meaningful solution to divergent power series, in order to assign finite values to divergent integral of certain transcendental functions $f(x)$. The functions are assumed to be analytical and hence they have a convergent Maclaurin series with infinity radius of convergence. Using Maclaurin series and binomial expansion, we equivalently convert the divergent integral to an infinite series in terms of Riemann zeta function. It is shown that the infinite series is convergent under a certain condition and consequently the solution of the divergent integral becomes $\int_0^{\infty} f(x) dx = \sum_{k=0}^{\infty} \frac{(-1)^{k+1}}{(k+2)!} f^{(k)}(0)$. The advantage of this Zeta regularization technique is that it does not not require introducing any cut-off function to calculate such divergent integrals. This formula is applied to calculate the divergent integral of several common transcendental functions.

math.NT↗

arXiv2021

Energy Efficient Control of Electric Motors

This paper presents development of an optimal feedback linearization control (OFLC) for interior permanent magnet (PM) synchronous machines operating in a non steady-sate operating point, i.e., varying torque and speed, to achieve precision tracking performance and energy saving by minimizing the copper loss. An isomorphism mapping between the dq-axes phase voltages and two auxiliary control inputs over full ranges of torque and speed is established by the linearization controller using the notion of orthogonal projection. The auxiliary control inputs are defined to be exclusively responsible for torque generation and power consumption. Subsequently, an analytical solution for the optimal-linearization control is derived in a closed-form by applying the Hamiltonian of optimal control theory in conjunction with the Pontryagin's minimum principle. The optimal controller takes the maximum voltage limit and torque tracking constraint into account while maximizing machine efficiency for non-constant operational load torque and speed. Unlike the convectional quadratic regulator-based control of electric motors, the proposed control approach does not rely on steady-state operation conditions and hence it is suitable for such applications as electric vehicles and robotics.

eess.SY↗

arXiv2021

Non-Minimal Systems with Switching Topology: Dynamics and Controls

This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this model describing dynamics of the dependent coordinates are: i) The mass matrix $\bar{M}(q)$ is always positive definite even at singular configurations; ii) matrix $\dot{\bar M} - 2 \bar{C}$ is skew symmetric, where all nonlinear terms are lumped into vector $\bar{C}(q, \dot q) \dot q$ after elimination of constraint forces. Eigenvalue analysis shows that the condition number of the constraint mass matrix can be minimized upon adequate selection of a scalar parameter called ``virtual mass'' thereby reducing the sensitivity to round-off errors in numerical computation. It follows by derivation of two oblique projection matrices for computation of constraint forces and actuation forces. It is shown that projection-based model allows feedback control of dependent coordinates which, unlike reduced-order dependent coordinates, uniquely define spatial configuration of constrained systems.

eess.SY↗

arXiv2021

Frictional Impacts in Multibody Systems

A unifying slipping and sticking frictional impact model for multibody systems in contact with a frictional surface is presented. It is shown that the model can lead to energetic consistency in both slip state and stick state upon imposing specific constraints on the coefficient of friction (CoF) and the coefficient of restitution (CoR). A discriminator in the form of a quadratic function of the pre-impact velocity is introduced based on isotropic Coulomb constraint such that its sign determines whether the impact occurs in the sticking mode or in the slipping mode just prior to the contact. Solving the zero-crossings of such a function in terms of the CoF and the CoR variables leads to another discriminator called Critical CoF, which is the lowest static CoF required to prevent the subsequent impulse vector violating the isotropic friction cone constraint. Investigating conditions for the energetically consistent impact model reveals that the maximum values of either CoR or CoF should be limited depending on stick state or slip state. Furthermore, it is shown that these upper-bound limits in conjunction with the introduced Critical CoF variable can be used to specify the admissible set of CoR and CoF parameters, which can be represented by two distinct regions in the plan of CoF versus CoR.

cond-mat.soft↗

arXiv2021

Nonsmooth Mechanics Based on Linear Projection Operator

This paper presents a unifying dynamics formulation for nonsmooth multibody systems (MBSs) subject to changing topology and multiple impacts based on linear projection operator. An oblique projection matrix ubiquitously derives all characteristic variables of such systems as follow: i) The constrained acceleration before jump discontinuity from projection of unconstrained acceleration, ii) post-impact velocity from projection of pre-impact velocity, iii) impulse during impact from projection of pre-impact momentum, iv) generalized constraint force from projection of generalized input force, and v) post-impact kinetic energy from pre-impact kinetic energy based on projected inertia matrix. All solutions are presented in closed-form with elegant geometrical interpretations. The formulation is general enough to be applicable to MBSs subject to simultaneous multiple impacts with non-identical restitution coefficients, changing topology, i.e., unilateral constraints becomes inactive or vice versa, or even when the overall constraint Jacobian becomes singular. Not only do the solutions always exist regardless the constraint condition, but also the condition number for a generalized constraint inertia matrix is minimized in order to reduce numerical sensitivity in computation of the projection matrix to roundoff errors. The model is proven to be energetically consistent if a global restitution coefficient is assumed. In the case of non-identical restitution coefficients, the set of energetically consistent restitution matrices is characterized by using Linear Matrix Inequality (LMI).

math.OC↗

arXiv2021

Analytical Mechanics With Quasi-Velocities

This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky decomposition of the mass matrix in conjunction with adequate orthogonal matrices are used to define reduced-quasi velocities, input quasi-forces, and constraint quasi-forces which possess natural metric. The new state and input variables always have homogeneous units despite the generalized coordinates may involve in both translational and rotational components and the constraint wrench may involve in both force and moment components. Therefore, this formulation is inherently invariant with respect to changes in dimensional units without requiring weighting matrices. Moreover, in this formulation the equations of motion are completely decoupled from those of constrained force. This allows the possibility of a simple force control action that is totally independent of the motion control action facilitating a hybrid force/motion control. The properties of the new dynamics formulation are investigated and subsequently, force/motion tracking control and regulation of constrained multibody systems based on quasi-velocities and quasi-forces are presented.

physics.comp-ph↗

arXiv2018

Analytical Solution to Improper Integral of Divergent Power Functions Using The Riemann Zeta Function

This paper presents an analytical closed-form solution to improper integral $μ(r)=\int_0^{\infty} x^r dx$, where $r \geq 0$. The solution technique is based on splitting the improper integral into an infinite sum of definite integrals with successive integer limits. The exact solution of every definite integral is obtained by making use of the binomial polynomial expansion, which then allows expression of the entire summation equivalently in terms of a weighted sum of Riemann zeta functions. It turns out that the solution fundamentally depends on whether or not $r$ is an integer. If $r$ is a non-negative integer, then the solution is manifested in a finite series of weighted Bernoulli numbers, which is then drastically simplified to a second order rational function $μ(r)=(-1)^{r+1}/(r+1)(r+2)$. This is achieved by taking advantage of the relationships between Bernoulli numbers and binomial coefficients. On the other hand, if $r$ is a non-integer real-valued number, then we prove $μ(r)=0$ by the virtue of the elegant relationships between zeta and gamma functions and their properties.

math.CA↗