In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V ≈ 1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: V max = 1 m / s , A max = 2 m / s 2 , and J max = 5 m / s 3 . In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

This paper presents a new method to increase the measurement resolution of quadrature encoders. The method contains an adaptive signal correction step and a signal interpolation step. Measured encoder signals contain imperfections including amplitude differences, mean offsets, and quadrature phase shift errors. With the proposed method, these errors are first corrected by using recursive least squares (RLS) estimation with exponential forgetting and resetting. Then, the corrected signals are interpolated to higher order sinusoids using a quick access look-up table generated offline. The position information can be obtained with the conversion of these high-order sinusoids to binary pulses and counting the zero crossings. Using the method presented here, a 10 nm measurement resolution is obtained using an encoder with 1 μm off-the-shelf resolution. Validation of the method and the practical limitations are also presented. Further increase in the resolution can be achieved by minimizing the effects of the electrical noise.

This paper presents a kinetostatic modeling framework for flexible cannulas (concentric tubing robots) subject to tip loads. Unlike existing methods that allow fast computation of the beam tip position, this modeling framework provides fast computation of both the tip position and the entire shape of the deflected robot. A method for online force sensing based on inverse kinetostatic solution is also proposed and assistive telemanipulation control methods for microstent delivery are presented. The modeling framework uses polynomial approximation and linear interpolation based on elliptic integral solutions to the deflection of lightweight beams. To date, there are no systems capable of stent delivery in retinal vasculature. The modeling and control frameworks of this paper are validated experimentally on pilot studies for microstent delivery. We believe that the methods presented in this paper open the way for robot-assisted retinal microvascular stenting that may potentially revolutionize the treatment of blinding retinal vasculature diseases.

This paper demonstrates the design of H ∞ loop-shaping controller for a linear time invariant (LTI) system with input saturation constraint. The design problem has been formulated in the four-block H ∞ synthesis framework, which is equivalent to normalized coprime factor robust stabilization problem. The shaped plant is represented as a polytopic linear parameter varying (LPV) system while saturation nonlinearity is considered. For a polytopic model, the LTI H ∞ loop-shaping controllers have been designed at each vertex of the polytope using linear matrix inequalities, and subsequently controllers are scheduled by adopting a certain interpolation procedure. The proposed controller ensures the stability and robust L 2 -performance of the closed-loop system due to vertex property of the polytopic LPV shaped plant. The effectiveness of the design method has been illustrated through a numerical example.

This paper examines the gain-scheduling problem with a particular focus on controller interpolation with guaranteed stability of the nonlinear closed-loop system. For linear parameter varying model representations, a method of interpolating between controllers utilizing the Youla parametrization is proposed. Quadratic stability despite fast scheduling is guaranteed by construction, while the characteristics of individual controllers designed a priori are recovered at critical design points. Methods for reducing the state dimension of the interpolated controller are also given. The capability of the proposed approach to guarantee stability despite arbitrarily fast transitions leads naturally to application to switched linear systems. The efficacy of the method is demonstrated in simulation using a multi-input, multi-output, nonminimum-phase system, while interpolating between two controllers of different sizes and structures.

A torque converter lock-up clutch slip control system, which is designed to improve fuel economy, must be able to precisely regulate slip speed. Also the system must have a high level of robustness for coping with changes in the operating conditions and any deterioration in the automatic transmission fluid and the clutch. Moreover, to reduce the design time, the design process must be as simple as possible. In this paper, we first propose a loop shaping that aims to optimize complementary sensitivity function of the control system, while satisfying the abovementioned requirements of performance and robustness. Next, a method for simplifying the design process is proposed, that is, a model and a controller are expressed by interpolation. A controller set, which has a relationship of duality to the interpolation parameters of the model, is created in advance so that the construction of a new control system can be realized by identifying the characteristic parameters only. From application to the actual design process for a vehicle, we verified that the design time was reduced to less than 1 ∕ 3 of that required for the conventional method. This new method has already been adopted for the design and fitting of new products.

A primary focus of the system dynamics literature is the development of structured modeling methods, suitable for application to a diverse array of engineering problems. An important obstacle in the development of unified modeling methods is the need to employ Eulerian reference frames in many thermofluid systems applications. An extension of Lagrange’s equations, to compressible thermofluid dynamics in Eulerian frames, offers a general modeling methodology for thermofluid systems compatible with discrete energy methods widely used for mechanical systems simulations.

This paper proposes a finite series expansion to approximate general nonlinear dynamics models to arbitrary accuracy. The method produces an approximation of nonlinear dynamics in the form of an aggregate of linear models, weighted by unimodal basis functions, and results in a linear growth bound on the approximation error. Furthermore, this paper demonstrates that the proposed approximation satisfies the modeling assumptions for analysis based on linear matrix inequalities and hence widens the applicability of these techniques to the area of nonlinear control.

In this work we introduce a methodology for the design of multivariable gain-scheduled controllers for nonlinear systems and an approach for determining the local stability of a nonlinear closed loop system. The gain-scheduled global control is designed by scheduling different local controllers using a Local Controller Network. The individual local controllers are assumed to be LTI MIMO controllers that can be designed via some user-specified multivariable method. In this paper, different portions of outputs from different local controllers are combined into the total control by using interpolation-weighting functions. The variation in the control behavior as a result of the scheduling variable is posed in a robust control framework. The dynamics of the scheduling variables are incorporated into the global control framework as an unstructured uncertainty. This allows the use of computational tools to analyze the stability of the overall global system and verify whether or not a given gain-scheduled approach will remain stable locally. To demonstrate the practical significance of the method, a multivariable electrohydraulic earthmoving powertrain problem is solved using the approach. The nonlinear power train was locally modeled as an LTI MIMO system and a local LTI MIMO controller was designed at each operating point using an H ∞ algorithm. The analysis approach introduced is utilized to verify system stability and is supported closely by experimental results.

Advanced control systems require accurate process models, while processes are often both nonlinear and time variant. After introducing the identification of nonlinear processes with grid-based look-up tables, a new learning algorithm for on-line adaptation of look-up tables is proposed. Using a linear regression approach, this new adaptation algorithm considerably reduces the convergence time in relation to conventional gradient-based adaptation algorithms. An application example and experimental results are shown for the learning feedforward control of the ignition angle of a spark ignition engine.

This paper presents an intelligent digital image correlation technique that uses genetic algorithms to measure surface displacements and strains. Speckle patterns are spray painted on the surface of interest and pictures taken before and during loading. Subpixel resolution, required for measuring displacements and strains accurately, is obtained by using interpolation methods. An innovative procedure based on genetic algorithms (GA) is used that has the potential to give the two displacements and four deformation gradients directly for a subset being investigated. This paper presents the algorithm for the six variables, but uses only the displacements (two variables) to calculate the 2-D strain fields. The genetic algorithms can guarantee a solution based on a comprehensive calibration procedure. The focus of this paper is the description of the GA routine used for the search process as well as the calibration scheme. Measurement results are presented for rigid-body displacement, 1-D and 2-D strain as proof of concept. Some potential applications for this work are to extract surface displacements and strains on the surfaces of aircraft, spacecraft and reusable launch vehicles, submarine and ship hulls, civil infrastructures such as bridges, dams and buildings, and biomedical imaging applications.

The competition to deliver fuel efficient and environmentally friendly vehicles is driving the automotive industry to consider even more complex powertrain systems. Adequate performance of these new highly interactive systems can no longer be obtained through traditional approaches, which are intensive in hardware use and final control software calibration. This paper explores the use of Dynamic Programming to make model-based design decisions for a lean burn, direct injection spark ignition engine, in combination with a three way catalyst and an additional three-way catalyst, often referred to as a lean NO X trap. The primary contribution is the development of a very rapid method to evaluate the tradeoffs in fuel economy and emissions for this novel powertrain system, as a function of design parameters and controller structure, over a standard emission test cycle.

The contouring accuracy of a multi-axis machine has a critical effect on the quality of many advanced technology products. One of the best approaches to assessing the contouring performance of machine tools is through double ball bar measurement. During circular interpolation motion, the machine traverses, with two axes at a time, a circular trajectory, with each axis subject to sinusoidal changes in acceleration, velocity, and position. The motion error is measured by detecting the relative distance between a point on the spindle nose and another point on the machine table and plotting this distance in polar coordinates. The present paper derives mathematical models and diagnosis procedures for first and second-order motion error resulting from the active degrees of freedom of a multi-axis machine. The theoretical results are verified by both computer simulation and double ball bar testing experiments.

Particle methods offer an efficient modeling approach to number of impact dynamics problems not well suited to conventional Eulerian finite difference or Lagrangian finite element methods. Unfortunately, the most popular of these particle methods (smooth particle hydrodynamics) exhibits important deficiencies, in part related to its treatment of boundaries and interparticle tension, and suffers from a rather ad hoc model formulation approach. A hybrid particle-element kinematic scheme and an energy-based, bond graph modeling approach have been combined to produce a new impact dynamics simulation method, free of many problems which have hindered the effective application of various particle and continuum methods. [S0022-0434(00)00602-X]

Passivity based control has several advantages, e.g., robustness and simplicity. However, the passivity constraint causes performance degradations. Specifically, the degree to which passively controlled absorber systems yield a flat response around the nominal absorber frequency is limited. An inherent flatness bound is derived using Nevanlinna-Pick boundary interpolation theory. For active vibration absorbers, this limitation cancels, and magnitude response can be made arbitrarily flat.

In this paper, we discuss a method of system identification based on Interpolated Mapping (IM). The method assumes the presence of sampled values of system states, based on which a map is defined that takes a set of initial conditions to their respective images. Using this map with time step T, maps with time steps T/2, T/4, …, are subsequently found. Ultimately, when the time step has become small enough, difference quotients are used to estimate the state derivatives. A function fit can then be applied to these derivatives in order to obtain the equations of motion of the system. The methodology of IM is used to approximate the images of states that are not on the primary grid. The above scheme works for autonomous systems because a single map can be used to follow the progress of the system at all times; the vector field of the system is invariant with time. However, the procedure breaks down when the system is forced. In this case, time enters the equations of motion explicitly, and different vector fields (and, hence, different maps) exist at different times. We show in this paper that the necessary modifications to the basic methodology are relatively minor. The work and storage requirements can increase by as little as a factor of two, regardless of the dimension of the state space. This is essentially a result of the fact that IM may be used to perform interpolation in the time direction, as well. However, when the forcing is such that its variation over time is entirely unknown, more data would be required to correctly observe its progress over the time period of interest. Functions of time that are flat for small times also necessitate additional effort for proper identification.

A new modal identification method for Conservative Nongyroscopic Systems is proposed. The modal identification method is formulated as a variational problem in which stationary values of a functional quotient are sought. The computation of the functional quotient is carried out using a set of admissible functions defined over the spatial domain of the system. Measurements of the free system response at discrete points are carried out using any combination of displacements, velocities, and/or accelerations. Three types of admissible functions have been considered—global functions, spatial Dirac-delta functions, and finite element interpolation functions. The variational modal identification method is applied to a pure bending vibration problem, to a pure longitudinal vibration problem, and to a combined bending and longitudinal vibration problem. The effectiveness of the variational modal identification method using different sets of admissible functions is examined.