A time‐varying coefficient‐based manipulability‐maximizing scheme for motion control of redundant robots subject to varying joint‐velocity limits

A time‐varying coefficient‐based manipulability‐maximizing (TVCMM) scheme subject to varying joint‐velocity limits (VJVL) is proposed and investigated in this paper for the optimal motion control of redundant robot manipulators (where a planar robot manipulator is specifically considered). In order to improve the manipulability during the end‐effector task execution, a manipulability‐maximizing index is considered into the scheme formulation. Besides, for the remedy of the nonzero initial/final joint‐velocity problem, a time‐varying coefficient is introduced and incorporated in the scheme, which is further reformulated as a quadratic program (QP) subject to equality and bound constraints. For guaranteeing the physical realizability of such a scheme, an efficient linear variational inequality‐based (LVI‐based) numerical algorithm is employed to solve such a QP, and an experiment based on a 6‐DOF manipulator is presented, of which the redundancy is on the horizontal plane. Simulative and experimental results validate the physical realization, effectiveness, and accuracy of the proposed QP‐based manipulability‐maximizing scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Expanded proximate time‐optimal servo control of permanent magnet synchronous motor

This paper extends the existing proximate time‐optimal servomechanism control methodology to the more typical second‐order servo systems with a damping element. A parameterized design of expanded proximate time‐optimal servomechanism control law with a speed‐dependent linear region is presented for rapid and smooth set‐point tracking using a bounded input signal. The control scheme uses the time‐optimal bang‐bang control law to accomplish maximum acceleration or braking whenever appropriate and then smoothly switches into a linear control law to achieve a bumpless settling. The closed‐loop stability is analyzed, and then the control scheme is applied to the position–velocity control loop in a permanent magnet synchronous motor servo system for set‐point position regulation. Numerical simulation has been conducted, followed by experimental verification based on a TMS320F2812 digital signal controller board. The results confirm that the servo system can track a wide range of target references with superior transient performance and steady‐state accuracy. Copyright © 2015 John Wiley & Sons, Ltd.     

On the synthesis of time‐varying LQG weights and noises along optimal control and state trajectories

A general approach to control non‐linear uncertain systems is to apply a pre‐computed nominal optimal control, and use a pre‐computed LQG compensator to generate control corrections from the on‐line measured data. If the non‐linear model, on which the optimal control and LQG compensator design is based, is of sufficient quality, and when the LQG compensator is designed appropriately, the closed‐loop control system is approximately optimal. This paper contributes to the selection and computation of the time‐varying LQG weighting and noise matrices, which determine the LQG compensator design. It is argued that the noise matrices may be taken time‐invariant and diagonal. Three very important considerations concerning the selection of the time‐varying LQG weighting matrices are turned into a concrete computational scheme. Thereby, the selection of the time‐varying LQG weighting matrices is reduced to selecting three scalar design parameters, each one weighting one consideration. Although the three considerations seem straightforward they may oppose one another. Furthermore, they usually result in time‐varying weighting matrices that are indefinite, rather than positive (semi) definite as required for the LQG design. The computational scheme presented in this paper addresses and resolves both problems. By two numerical examples the benefits of our optimal closed‐loop control system design are demonstrated and evaluated using Monte Carlo simulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

This work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case. The Laguerre functions are used to simplify and enhance the control horizon effect through parsimonious control trajectory, thus reducing the computational load required to find the optimal control solution. Furthermore, these results can be confirmed by simulations and experimental tests on the manipulator and comparing it to the traditional DMPC approach and the discrete linear quadratic regulator.     

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

In this paper, learning control is integrated with non‐linear optimal control to enhance control performance of a class of non‐linear systems with time‐varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function (CLF) and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non‐linear dynamic system. The proposed learning mechanism learns the unknown time‐varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function (CEF). The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon. Copyright © 2001 John Wiley & Sons, Ltd.     

A 2D‐based approach to guaranteed cost repetitive control for uncertain discrete‐time systems

This paper presents a two‐dimensional (2 D)‐based approach to the problem of guaranteed cost repetitive control for uncertain discrete‐time systems. The objective is to design a control law such that the closed‐loop repetitive control system is robustly stable and a certain bound of performance criteria is guaranteed for all admissible uncertainties. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2 D system. Then, sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal guaranteed cost control law by minimizing the upper bound of the cost function. The proposed approach is applicable not only to SISO systems, but also to MIMO systems. Two numerical examples are provided to demonstrate the effectiveness of the proposed controller design procedures. Copyright © 2010 John Wiley & Sons, Ltd.     

Low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling

This paper presents the low‐order multi‐rate linear time‐invariant decentralized trackers using the new observer‐based sub‐optimal method for a class of unknown sampled‐data nonlinear time‐delay system with closed‐loop decoupling. For the unknown sampled‐data nonlinear time‐delay system, we assume that the inner time delay is clearly known. Under this prerequisite, the appropriate (low‐) order decentralized linear observer for the unknown sampled‐data nonlinear system is determined by the off‐line observer/Kalman filter identification (OKID) method with artificial delay input and actual delay output. Then, the above observer has been further improved based on the proposed new observer‐based sub‐optimal approach. Sequentially, the decentralized tracker with the high gain property is proposed, so that the closed‐loop system has the decoupling property. The proposed approach constructs complete mathematics method including the concept of optimal control theory and state‐matching digital redesign technique and is quite useful for the complicated interconnected large‐scale sampled‐data nonlinear time‐delay system with unknown system equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems

Minimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal fixed‐levels control for nonlinear systems with quadratic cost‐functionals

This paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous‐time switched systems in the presence of some specific control constraints. The stepwise (fixed‐level type) control restrictions we consider constitute a common class of admissible controls in many real‐world engineering systems. Moreover, these control restrictions can also be interpreted as a result of a quantization procedure appglied to the inputs of a conventional dynamic system. We study control systems with a priori given time‐driven switching mechanism in the presence of a quadratic cost functional. Our aim is to develop a practically implementable control algorithm that makes it possible to calculate approximating solutions for the class of OCPs under consideration. The paper presents a newly elaborated linear quadratic‐type optimal control scheme and also contains illustrative numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

An efficient scheme for minimax solutions of multiple linear‐quadratic control

Optimal control is one of the most important methodologies for studies of dynamic systems in many areas of sciences, engineering and economics. Minimax optimal control is a special topic in the general framework of multiple optimal control problems. Minimax optimal control can be considered as a dynamic game with multiple players under the same system. In this paper, we develop a fast search for a minimax solution of multiple linear‐quadratic control problems. The algorithm improves the existing solution scheme by adjusting the multiple weighting coefficients in each iteration and also including updates for step‐size control. Copyright © 2005 John Wiley & Sons, Ltd.     

An MPC‐based position controller for a tilt‐rotor tricopter VTOL UAV

This study presents a novel framework, namely, the fusion of a conventional controller and a linear model predictive controller, for the position control of a tilt‐rotor tricopter. While the conventional controller in the outer loop is responsible for the position control, the inner‐loop model predictive control–based controller handles the angular dynamics and vertical body velocity. Furthermore, a novel control allocation algorithm for the proposed controller is introduced. In addition, this study also covers mathematical modeling and trim analysis of the tilt‐rotor tricopter dynamics. An evaluation of the designed control system is accomplished with a nonlinear 6‐degree‐of‐freedom simulation model of the tilt‐rotor tricopter in which realistic actuator limitations are considered. The efficiency of the proposed control algorithm is elaborated for a trajectory tracking problem where basic surveillance operation is considered. The simulation results show that the proposed model predictive controller is able to provide a satisfactory trajectory tracking performance under the realistic actuator limits.     

Hamiltonian two‐degrees‐of‐freedom control of chemical reactors

A novel unified approach to two‐degrees‐of‐freedom control is devised and applied to a classical chemical reactor model. The scheme is constructed from the optimal control point of view and along the lines of the Hamiltonian formalism for nonlinear processes. The proposed scheme optimizes both the feedforward and the feedback components of the control variable with respect to the same cost objective. The original Hamiltonian function governs the feedforward dynamics, and its derivatives are part of the gain for the feedback component. The optimal state trajectory is generated online, and is tracked by a combination of deterministic and stochastic optimal tools. The relevant numerical data to manipulate all stages come from a unique off‐line calculation, which provides design information for a whole family of related control problems. This is possible because a new set of PDEs (the variational equations) allow to recover the initial value of the costate variable, and the Hamilton equations can then be solved as an initial‐value problem. Perturbations from the optimal trajectory are abated through an optimal state estimator and a deterministic regulator with a generalized Riccati gain. Both gains are updated online, starting with initial values extracted from the solution to the variational equations. The control strategy is particularly useful in driving nonlinear processes from an equilibrium point to an arbitrary target in a finite‐horizon optimization context. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal control of human‐like musculoskeletal arm: Prediction of trajectory and muscle forces

Optimal trajectory and muscle forces of a human‐like musculoskeletal arm are predicted for planar point‐to‐point movements using optimal control theory. The central nervous system (CNS) is modeled as an optimal controller that performs a reaching motion to final states via minimization of an objective function. For the CNS strategy, a cubic function of muscles stresses is considered as an appropriate objective function that minimizes muscles fatigue. A two‐DOF nonlinear musculoskeletal planar arm model with four states and six muscle actuators is used for the evaluation of the proposed optimal strategy. The nonlinear variational formulation of the corresponding optimal control problem is developed and solved using the method of variation of extremals. The initial and (desired) final states (position and velocity) are used as input kinematic information, while the problem constraints include the motion range of each joint, maximum allowable muscle tension, and stability requirements. The resulting optimal trajectories are compared with experimental data as well as those corresponding to recent researches on model predictions of human arm movements. It is demonstrated that the proposed optimal control strategy using minimum fatigue criterion is more realistic in prediction of motion trajectories in comparison with previous work that has utilized minimum joints' torque criterion. Accordingly, minimization of muscles fatigue is an effective biomechanical criterion for the CNS in prediction of point‐to‐point human arm motions. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal control of linear multi‐delay systems based on a multi‐interval decomposition scheme

This paper presents a novel approximation scheme to the numerical treatment of linear time‐varying multi‐delay systems with a quadratic performance index. A direct approach based on a hybrid of block‐pulse functions and Chebyshev polynomials is successfully developed. The operational matrix of delay associated to multi‐delay systems is constructed by an efficient manner. The excellent properties of hybrid functions together with the operational matrices of integration, delay, and product are then used to transform the optimal control problem into a mathematical optimization problem whose solution is much more easier than the original one. The procedure described in the current paper can be regarded as a multi‐interval decomposition scheme. The convergence of the proposed method is verified numerically. A wide variety of multi‐delay systems are investigated to demonstrate the effectiveness and computational efficiency of the proposed numerical scheme. The method has a simple structure, is easy to implement, and provides very accurate solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

In vivo kinematics and kinetics of a bi‐cruciate substituting total knee arthroplasty: A combined fluoroscopic and gait analysis study

After total knee arthroplasty, changes in articular surface geometry, soft tissue treatment, and component alignment can alter normal lower limb function. The guided motion bi‐cruciate substituting prosthesis was designed specifically to restore physiological knee joint motion. We determined whether this design could in vivo normal kinematics and kinetics, not only at the replaced knee, but also throughout both lower limbs. Sixteen patients (4 male, 12 female, mean age of 68.2 years with a range from 58 to 79 years) with primary knee osteoarthritis were implanted with the bi‐cruciate substituting prosthesis. At 6‐month follow‐up, knee joint kinematics was assessed by video‐fluoroscopy during stair‐climbing, chair‐rising/sitting, and step‐up/down. Lower limb overall function was also assessed on the same day by standard gait analysis with simultaneous electromyography during level walking. By video‐fluoroscopy, mean anteroposterior translations between femoral and tibial components during the three motor tasks were 9.7 ± 3.0, 10 ± 2.6, and 6.9 ± 3.5 mm on the medial compartment, and 14.3 ± 3.5, 18.5 ± 3.0, and 13.9 ± 3.8 mm on the lateral compartment, respectively. Axial rotation ranged from 5.6° to 26.2°. Gait analysis revealed restoration of nearly normal walking patterns in most patients. This rare combination of measurements, i.e., accurate rotation‐translation at the replaced knee and complete locomotion patterns at both lower limb joints, suggested that bi‐cruciate substituting arthroplasty can restore physiological knee motion and normal overall function. © 2009 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 27:1569–1575, 2009     

Online identifier–actor–critic algorithm for optimal control of nonlinear systems

In this paper, a novel identifier–actor–critic optimal control scheme is developed for discrete‐time affine nonlinear systems with uncertainties. In contrast to traditional adaptive dynamic programming methodology, which requires at least partial knowledge of the system dynamics, a neural‐network identifier is employed to learn the unknown control coefficient matrix working together with actor–critic‐based scheme to solve the optimal control online. The critic network learns the approximate value function at each step. The actor network attempts to improve the current policy based on the approximate value function. The weights of all neural networks are updated at each sampling instant. Lyapunov theory is utilized to prove the stability of closed‐loop system. It shows that system states and neural network weights are uniformly ultimately bounded. Finally, simulations are provided to illustrate the effectiveness of the developed method. Copyright © 2016 John Wiley & Sons, Ltd.     

In Vitro Evaluation of the Dual‐Diffuser Design for a Reversible Rotary Intra‐Aortic Ventricular Assist Device

The intra‐aortic ventricular assist device (IntraVAD) is a miniature intra‐aortic axial‐flow ventricular assist device (VAD) that works in series with the left ventricle (LV) to assist the compromised heart. Previous in vitro results have shown that the IntraVAD can successfully increase coronary perfusion and offload ventricular volume by operating in reverse‐rotation control (RRc) mode. The RRc mode includes forward rotation in systole and reverse rotation (RR) in diastole. It is necessary to derive a new diffuser design that can be used for the bi‐directional rotation of the IntraVAD. In this work, a dual‐diffuser set (DDS) was proposed to replace the conventional inducer and diffuser upstream and downstream of the pump. The DDS comprised two diffusers, located on both sides of the impeller, omitting the conventional inducer and diffuser. Different configurations of the DDS were designed and manufactured with various combinations of curved and straight blades. All configurations were initially tested in continuous flow, then in a pulsatile mock circulatory loop. A weighted normalized scalar (WNS) was proposed to comprehensively evaluate the hemodynamic effect of the DDS with different configurations. The results show that the maximum of WNS occurred when the upstream diffuser had equal numbers of curved and straight blades and the downstream diffuser had only curved blades. This indicates such a dual‐diffuser design for the IntraVAD can give an optimal cardiac assistance potentially improving ventricular contractility, thereby restoring heart function.     

Adjoints estimation methods for impulsive Moon‐to‐Earth trajectories in the restricted three‐body problem

A study of optimal impulsive Moon‐to‐Earth trajectories is presented in a planar circular restricted three‐body framework. Two‐dimensional return trajectories from circular lunar orbits are considered, and the optimization criterion is the total velocity change. The optimal conditions are provided by the optimal control theory. The boundary value problem that arises from the application of the theory of optimal control is solved using a procedure based on Newton's method. Motivated by the difficulty of obtaining convergence, the search for the initial adjoints is carried out by means of two different techniques: homotopic approach and adjoint control transformation. Numerical results demonstrate that both initial adjoints estimation methods are effective and efficient to find the optimal solution and allow exploring the fundamental tradeoff between the time of flight and required ΔV. Copyright © 2014 John Wiley & Sons, Ltd.     

Trajectory planning of a free‐flying robot by using the optimal control

In this paper, we consider the planar motion of a free‐flying robot equipped with the jet thrust mechanism. Based on the non‐linear equations of motion of the free‐flying robot, we calculate the optimal control such that the fuel consumption is minimized and that the given terminal condition is satisfied at the end of motion. We use Sakawa–Shindo algorithm for calculating the optimal control, which was derived on the basis of Pontryagin's maximum principle. The computational results are satisfactory and show that the algorithm works well. Copyright © 1999 John Wiley & Sons, Ltd.     

An efficient intensity‐based ready‐to‐use X‐ray image stitcher

Background: The limited field of view of the X‐ray image intensifier makes it difficult to cover a large target area with a single X‐ray image. X‐ray image stitching techniques have been proposed to produce a panoramic X‐ray image. Methods: This paper presents an efficient intensity‐based X‐ray image stitcher, which does not rely on accurate C‐arm motion control or auxiliary devices and hence is ready to use in clinic. The stitcher consumes sequentially captured X‐ray images with overlap areas and automatically produces a panoramic image. The gradient information for optimization of image alignment is obtained using a back‐propagation scheme so that it is convenient to adopt various image warping models. Results: The proposed stitcher has the following advantages over existing methods: (1) no additional hardware modification or auxiliary markers are needed; (2) it is robust against feature‐based approaches; (3) arbitrary warping models and shapes of the region of interest are supported; (4) seamless stitching is achieved using multi‐band blending. Experiments have been performed to confirm the effectiveness of the proposed method. Conclusion: The proposed X‐ray image stitcher is efficient, accurate and ready to use in clinic.