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A novel manipulation control framework is proposed for the dexterous robotic hand, which integrates the constraints (contact constraints and servo constraints), dynamics modeling and controller design. In the manipulation task, the contact between the robotic hand and the target object translates the manipulating force and constraints the relative motion of the target. Hence, the contact forces can be considered as the bridge for the robotic hand manipulation and the motion control of the target object. By the Udwadia-Kalaba theory, the dynamics model of the contact forces for the rolling manipulation in the work space is constructed explicitly without any auxiliary variable and calculated by the states of the robotic hand (such as, the angular and velocity of the finger joints) and the local variables of the target object (e.g., the surface parameters). Based on the formulated contact forces, an integrated control strategy is introduced to tackle with the manipulation task by combining the desired motion of the target object and the manipulation controller design through the contact constraints. Virtue of the calculated contact forces, the proposed control could accomplish the manipulation tasks without force sensors. Besides, to ensure the trajectory of the object is smooth and continuous, a grasping plan for the dexterous robotic hand is proposed. The effectiveness of the control is verified by both theoretical proof and the numerical simulation of a three fingered robotic hand in 3D workspace.

The robust bounded control problem for the permanent magnet linear motors with inequality constraints is studied. Firstly, the dynamical model of the system is built, through the state transformation is used to satisfy the inequality constraint of the position output. Thus, the controller after the state transformation can ensure that the control output of the linear motor stays the desired range. Selecting the appropriate boundary function, and then the upper and lower bounds of the control output can be set according to our control requirements. The control scheme can guarantee uniform boundedness and uniform ultimate boundedness. The results of experiments and simulation show that the proposed algorithm can assure the control output within the desired range regardless of the uncertainty.

Abstract In this paper, a new fuzzy approach is applied to optimal design of the anti-skid control for electric vehicles. The anti-skid control is used to maintain the wheel speed when there are uncertainties. The control is able to provide an appropriate torque for wheels when the vehicle is about to skid. The friction coefficient and the moments of inertia of wheels and motor are considered as uncertain parameters. These nonlinear, bounded and time-varying uncertainties are described by fuzzy set theory. The control is deterministic and is not based on IF-THEN fuzzy rules. Then, the optimal design for this fuzzy system and control cost is proposed by fuzzy information. In this way, the uniform boundedness and uniform ultimate boundedness are guaranteed and the average fuzzy performance is minimized. Numerical simulations show that the control can prevent vehicle skidding with the minimum control cost under uncertainties.

The current developed friction models are basically based on the assumption of the normal forces exerted between the contact surfaces known in advance, less work has been done for closed-form (i.e., analytic) modeling in complex mechanical systems where the normal forces vary greatly over time. In this paper, the closed-form representations of friction forces in mechanical systems are newly derived in a way of dynamics. The Udwadia-Kalaba equation is first used to calculate the normal force exerted by the contact surface in mechanical system. The friction force is then calculated via existing friction models. Such closed-form expressions of friction forces contain both the magnitude and direction at any instant of time, even as the normal force is nonconstant. The novel representations offer an effective way for analytically expressing friction force in dynamical systems, which makes it possible for accurate simulation and control design of dynamical systems with non-negligible friction forces.

This paper proposes an indirect approach of constraint-following control for mechanical systems with (possibly fast) time-varying uncertainty. It proposes to design controller for the system to render bounded constraint-following error. First, it prescribes a desired hard bound for the constraint-following error. The system is required to lie within the bound at all time. Second, the constraint-following error can eventually be sufficiently small. To accomplish this, the original system is transformed into a constructed system. Then a robust control for the constructed system is designed, with renders uniform boundedness and uniform ultimate boundedness, regardless of the uncertainty. It is further proven that when the constructed system is uniformly bounded and uniformly ultimately bounded, the constraint-following error of the original system stays within the pre-determined bounded. In addition, it will become sufficiently small after a finite time. Therefore the desired bounded performance of the constraint-following error can be archived by the robust control. Since the control is not designed based on the original system, the approach is indirect.

A series of fractional robust trajectory tracking controls are proposed for the Delta parallel robot with uncertainty. For the high speed and heavy load, the Delta parallel robot could not ignore the influences of the high nonlinearity (by the dynamics of the multiple closed-loops mechanism and the nonlinear joints friction) and the various kinds of uncertainties (i.e., the unknown dynamic parameters and external disturbances caused by the residual vibration). By formulating the motion equation of the Delta parallel robot, the nonlinearity is settled by a norm model based control design. The uncertainty considered in the paper is time-varying but unknown. An online estimation with an exponential type leakage term and dead-zone is construct to investigate the realtime information of the uncertainty. In virtue of the estimated information, two fractional robust trajectory tracking controls with the joints friction compensation are designed. Under the proposed controls, the system performance of the Delta parallel robot can be deterministically guaranteed (which includes uniform boundedness and uniform ultimate boundedness).

This paper is concerned with the control design for a class of stochastic nonlinear systems. Three uncertainties are considered; that is, nonlinear parameter uncertainty, matched uncertainty and stochastic disturbance. The nonlinear uncertainty contains some uncertain parameter and satisfies bound condition. Neither the exact value of the matched uncertainty nor its possible bound is known; its upper bound function satisfies certain concave condition. The stochastic disturbance is a standard Wiener process. Based on stochastic Lyapunov stability theory, the adaptive robust controller is designed, which renders the state variables of the closed-loop system bounded in probability, regardless of all uncertainties. The desired controller is constructed by the upper bound function and the saturation function, in which the upper bound function represents the magnitude of the control, while the saturation function indicates the control direction. The design of the adaptive robust controller is based on the minimum information of uncertainty, which is simple and can be easily realized in practical systems. Finally, a two-tank water level control example is used to demonstrate the effectiveness of our control design.

In this paper, we propose a novel practical robust control algorithm for the Selective Compliance Articulated Robot Arm (SCARA) robot and verify the effectiveness through experiments. The dynamic model of the SCARA robot is established considering uncertainties, which include the nonlinear friction, parameter uncertainty, and external disturbance. To restrain the reversal chattering, we apply a modified Stribeck friction model with Gaussian compensation term as the friction description. The algorithm is composed of a proportional-derivative (PD) feedback term based on the model and a robust term. The formation of the robust part comprises the upper bound of the uncertainty. The Lyapunov minimax method is adopted to prove that the system is uniformly bounded and uniformly ultimately bounded, thus guaranteeing the practical stability of the system. Moreover, rapid controller prototyping cSPACE, as the experimental platform, can eliminate the tedious programming work and provide a great convenience for the experiments. The experimental results indicate that the robust control algorithm has good performance, which provides accurate trajectory tracking under the influence of uncertainties.

A novel estimation-based and dropout-dependent control design for distributed control systems of aeroengines with packet dropout is proposed. The packet dropout is described as an independent identically distributed (i.i.d.) Bernoulli process with known probability. The objective of the control system is to effectively and stably impel aeroengines. An inverse system is proposed to reconstruct the missing measurements, based on which, a hybrid adaptive Kalman filter (HAKF) is proposed to provide the estimated states for control design. A new state-feedback control design is developed with the estimated states and the actual states. For guaranteeing the stability of aeroengines, both the stability of HAKF and the new controlled system are analyzed and proved. The new design is applied to an aeroengine, HAKF has superior estimation accuracy which ensures the effectiveness, and the desired stability performance is achieved by controlled system in the presence of packet dropout.

During the past three decades, the problems of reliable control and filtering have attracted considerable attention due to the growing demands for system safety, reliability, maintainability, and survivability. The main aim of reliable control and filtering is to design a suitable controller and filter with guaranteed stability and performance, respectively; not only when all the system components are in operation, but also when some component failures occur. To guarantee a higher reliability level and better control performance, reliable control systems depending on various control strategies have tried to achieve these critical requirements, i.e., the pole region assignment method, coprime factorization method, the algebraic Riccati equation (ARE)-based method, the Hamilton-Jacobi inequality (HJI)-based method, and linear matrix inequality (LMI)-based method. Although many researchers have investigated the reliable control/filtering problems for linear systems with different scenarios for many years, the topic of reliable control/filtering in complex nonlinear systems is still in the early stages of development and many critical issues remain to be further investigated.

A novel control scheme, namely adaptive-adaptive robust (A2R) control is proposed for motion control of mechanical systems. The system contains uncertainty which is bounded while the bound may be unknown. Two designs of robust controls are proposed, with the first class featuring leakage type and the second class featuring dead-zone type. Each class involves an adaptive law with the intension of mimicking the uncertainty bound. However, there exists an undetermined design parameter in the adaptive law. An upper-layer adaptive law for the determination of this design parameter is then proposed; hence rendering the adaptive-adaptive robust (A2R) control. The control guarantees uniform boundedness and uniform ultimate boundedness of a resulting augmented system state, including a β-measure which reflects how close the constraint is followed.

In this paper, we design an optimal robust control to address the problem of position tracking control for permanent magnet linear motor (PMLM). The uncertainties in PMLM system, including parameters uncertainty and external disturbance, are nonlinear and time-varying. The uncertainties are assumed to be bounded, and the bounds are described via fuzzy sets. Then, a model-based robust control in deterministic form is proposed. Furthermore, an optimal robust control for PMLM system is formulated as a fuzzy performance index optimization problem, which associated with both the fuzzy system performance and the control cost. The resulting optimal control can guarantee the uniform boundedness and uniform ultimate boundedness. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness of the optimal robust control for PMLM.

This paper proposes a hierarchical multivariable robust control design for a class of uncertain nonlinear dynamic system. The dynamic system is described by an uncertain T-S fuzzy model. The uncertainties in the model are structure matched and norm-bounded. For this fuzzy model, a hierarchical robust control consisting of two level compensators is presented. While the level 1 compensator ensures the basic robust performance, the level 2 compensator restrains the uncertainty. Under this design, the controlled system is uniformly bounded and uniformly ultimately bounded. To illustrate the design approach, the application to a multivariable control of turbofan engines is discussed. The semi-physical simulations of the controlled turbofan show that the resulting control is able to guarantee the prescribed boundedness in a more practical condition.

Abstract There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations.

The stabilization problem of a macroeconomic dynamical system is considered in this paper. The main features of this system are that the system uncertainties may be unknown functions of state and time but with known bounds. Furthermore, the control inputs are subject to constraints, which is a salient feature in an economic control problem. To ensure that the controls are within the specified boundaries, in our control design procedure, a creative diffeomorphism, which converts bounded controls into unbounded corresponding signals by choosing an appropriate transformation function, is proposed. For the uncertain system, a deterministic robust control is designed to render the practical stability: uniform boundedness and uniform ultimate boundedness. The range of the input bounds is related to the uncertainties and can be designed according to the actual situation. Numerical simulations are performed to verify the effectiveness of the stabilization policy.

High-speed Permanent Magnet Synchronous Motor (PMSM) systems have been widely used in industry and other fields for their advantages of having a simple structure, low processing cost and high efficiency. At present, the control precision of PMSM is required to be higher and higher, but it faces two major challenges. The first is that the PMSM system possesses (possibly fast) time-varying uncertainty. The second is that there exist nonlinear portions in the PMSM system, such as nonlinear elasticity, etc. To resolve these challenges, a novel performance measure β^ is introduced as a dynamic depiction of the constraint-following error, and a new robust control design is proposed based on β^. While this control renders guaranteed performance regardless of uncertainty, an optimal design of a control parameter is further pursued. This inquiry is summed up as a semi-infinite constrained optimization problem. After the induction of the necessary condition, the candidate solutions can be identified. These are further screened by a sufficient condition, which results in the actual solution. To verify the effectiveness of the control design, the compressor powered by a super high-speed PMSM system is simulated, and its performance is discussed.

The constraint following stabilization problem of aerospace mechanical manipulators containing uncertainty is investigated. Due to the inevitable modeling error and external disturbance, there always exists uncertainty. To guarantee that the mechanical system follows prescribed constraints (holonomic or non-holonomic), two classes of adaptive robust controls are proposed. The system performance is represented based on a $\varphi $ -measure. The control scheme consists of two parts: the nominal control part and the adaptive robust control part. By the Udwadia–Kalaba theory, the nominal control is proposed to force the nominal mechanical system to meet the constraints. Furthermore, the adaptive robust control is proposed to address the uncertainty issue, while the adaptation law is proposed to estimate the bounding information of the uncertainty. Under the control, the system is guaranteed to follow the constraint regardless of the uncertainty.

An optimal control design for the uncertain Delta robot is proposed in the paper. The uncertain factors of the Delta robot include the unknown dynamic parameters, the residual vibration disturbances and the nonlinear joints friction, which are (possibly fast) time-varying and bounded. A fuzzy set theoretic approach is creatively used to describe the system uncertainty. With the fuzzily depicted uncertainty, an adaptive robust control, based on the fuzzy dynamic model, is established. It designs an adaptation mechanism, consisting of the leakage term and the dead-zone, to estimate the uncertainty information. An optimal design is constructed for the Delta robot and solved by minimizing a fuzzy set-based performance index. Unlike the traditional fuzzy control methods (if-then rules-based), the proposed control scheme is deterministic and fuzzily optimized. It is proven that the global solution in the closed form for this optimal design always exists and is unique. This research provides the Delta parallel robot a novel optimal control to guarantee the system performance regardless of the uncertainty. The effectiveness of the proposed control is illustrated by a series of simulation experiments. The results reveal that the further applications in other robots are feasible.

In this paper, a H ∞ /Leitmann approach to the robust tracking control design is presented for an uncertain dynamic system. This new method is developed in the following two steps. Firstly, a tracking dynamic system with simultaneous consideration of parameter uncertainty and noise is modeled based on a linear system and a reference model. Accordingly, a “nominal system” from the tracking system is defined and controlled by a H ∞ control to obtain the asymptotical stability and noise resistance. Secondly, by making use of a Lyapunov function and the norm boundedness, a new robust control with the “Leitmann approach” is designed to cope with the uncertainty. The two controls collaborate with each other to achieve “uniform tracking boundedness” and “uniform ultimate tracking boundedness”. The new approach is then applied to an aircraft turbofan control design, and the numerical simulation results show the prescribed performances of the closed-loop system and the advantage of the developed approach.

The revolution of physical structure is highly significant for future software defined vehicles (SDV). Active structural transformation is a promising feature of the next generation of vehicle physical structure. It can enhance the dynamic performance of vehicles, thus providing safer and more comfortable ride experiences, such as the ability to avoid rollover in critical situations. Based on the active structural transformation technology, this study proposes a novel approach to improve the dynamic performance of a vehicle. The first analytical motion model of a vehicle with active structural transformation capability is established. Then, a multi-objective optimization problem with the adjustable parameters as design variables is abstracted and solved with an innovative scenario specific optimization method. Simulation results under different driving scenarios revealed that the active transformable vehicle applying the proposed method could significantly improve the handling stability without sacrificing the ride comfort, compared with a conventional vehicle with a fixed structure. The proposed method pipeline is defined by the software and supported by the hardware. It fully embodies the characteristics of SDV, and inspires the improvement of multiple types of vehicle performance based on the concept of "being defined by software" and the revolution of the physical structure. [ABSTRACT FROM AUTHOR]