Robotic Manipulators and Vehicles

The chapter analyzes the model-based nonlinear control approaches for multi-DOF rigid-link robots, that is (i) control based on global linearization methods, and (ii) control based on approximate linearization methods. As far as approach (i) is concerned, that is methods relying on global linearization, these are techniques for the transformation of the nonlinear dynamics of the robotic system to equivalent linear state-space descriptions for which one can design state feedback controllers and can also solve the associated state estimation (filtering) problem. One can classify here methods mainly elaborating on the theory of differentially flat systems. Differentially flat systems form the widest class of systems to which global linearization-based nonlinear control can be applied. As far as approach (ii) is concerned. solutions are sought to the problem of nonlinear control of robots with the use of local linear models (defined around local equilibria). For such local linear models, feedback controllers of proven global stability can be developed. One can select the parameters of such local controllers in a manner that ensures the robustness of the control loop to both external perturbations and to model’s parametric uncertainty. In particular the chapter develops the following topics: (a) Kinematics and dynamics of multi-DOF robotic manipulators. (b) Model-based control of rigid-link manipulators using global linearization methods, (c) Model-based control of rigid-link manipulators using approximate linearization methods, (d) Model-based control using global linearization methods for rigid-link manipulators subject to time-delays.

Control of underactuated robots has received significant attention and its application areas comprise several types of industrial and service robotic manipulators. The purpose of research in this area is to design robotic mechanisms that can be controlled despite having a number of actuators that is smaller than their degrees of freedom. This approach can reduce the cost and weight of robots or can provide robotic systems with tolerance to actuators failures. Again the control problem for such robots can be treated with (i) global linearization methods, (ii) approximate linearization approaches and (iii) Lyapunov methods. To achieve model-free control of underactuated manipulators, improved estimation approaches are developed, allowing the real-time identification of their unknown dynamics or kinematics. Moreover, to implement feedback control of underactuated robots through the measurement of a limited number of the robot’s state variables, nonlinear filtering methods of proven convergence are developed. In particular the chapter develops the following topics: (a) Nonlinear optimal control for multi-DOF underactuated overhead cranes, (b) Nonlinear optimal control for ship-mounted cranes (c) Nonlinear optimal control for the rotary (Furuta’s) pendulum, (d) Nonlinear optimal control for the cart and double-pendulum system, and (e) Nonlinear optimal control for a 3-DOF underactuated robotic arm

The chapter analyzes model-free nonlinear control approaches for multi-DOF rigid-link robots, based on Lyapunov methods. There, one comes against problems of minimization of Lyapunov functions so as to ensure the asymptotic stability of the control loop. Model-free control takes often the form of indirect adaptive control. In such a case the design of the controller is not based on prior knowledge of the robot’s dynamics. With the use of adaptive algorithms and elaborated estimation methods it is possible to identify in real-time the unknown dynamics of the robots and subsequently to use this information in the control loop, thus arriving at indirect adaptive control schemes. Finally, the development of nonlinear state-estimation methods for robotic manipulators allows the implementation of feedback control through measuring of only a small number of the robot’s state variables. Global stability is proven for the control loop that comprises both the nonlinear controller of the robot’s dynamics and nonlinear observers that estimate the robot’s state vector from indirect measurements. In particular, the chapter develops the following topics: (a) Model-free adaptive control of rigid-link manipulators using full-state feedback, (ii) Model-free adaptive control of rigid-link manipulators using output feedback, (iii) Model-free adaptive control of the underactuated rotary (Furuta’s) pendulum.

Control of closed-chain robots is a non-trivial problem because it is often associated with complicated dynamic and kinematics models exhibiting nonlinearities. Unlike robotic manipulators with a free end-effector, closed-chain robotic mechanisms include actuators which are usually placed on a fixed base. On the one side this enables to develop robotic and mechatronic systems with low moving inertia and fast motion control. On the other side this may incur underactuation problems. Comparing to open-chain robots, closed-chain robotic mechanisms have many advantages such as high stiffness, high accuracy, and high payload-to-weight ratio To solve the nonlinear control problem of closed-chain robotic systems the following approaches are proposed (i) nonlinear control based on global linearization methods, (ii) nonlinear control based on approximate linearization methods and (iii) nonlinear control based on Lyapunov methods. Besides to apply model-free control for such a type of robotic manipulators, online estimation algorithms of the unknown dynamics of the robot can be considered once again. The global asymptotic stability of the control based on the real-time estimation of the robot’s dynamics is proven. Moreover, as in the previously analysed multi-DOF manipulator models, to implement feedback control through the measurement of a limited number of the closed-chain robot’s state vector elements, nonlinear filtering methods of proven convergence are developed. In particular the chapter analyzes the following topics: (a) Model-based control of closed-chain kinematic mechanisms with the use of differential flatness theory, (b) Flatness-based adaptive fuzzy control of closed-chain kinematic mechanisms (c) Nonlinear optimal control for closed-chain kinematic mechanisms.

Control for flexible-link robots is a non-trivial problem that has elevated difficulty comparing to the control of rigid-link manipulators. This is because the dynamic model of the flexible-link robot contains the nonlinear rigid link motion coupled with the distributed effects of the links’ flexibility. This coupling depends on the inertia matrix of the flexible manipulator while the vibration characteristics are determined by structural properties of the links such as the damping and stiffness parameters. Moreover, in contrast to the dynamic model of rigid-link robots the dynamic model of flexible-link robots is an infinite dimensional one. As in the case of the rigid-link manipulators there is a certain number of mechanical degrees of freedom associated to the rotational motion of the robot’s joints and there is also an infinite number of degrees of freedom associated to the vibration modes in which the deformation of the flexible link is decomposed The controller of a flexible manipulator must achieve the same motion objectives as in the case of a rigid manipulator, i.e. tracking of specific joints position and velocity setpoints. Additionally, it must also stabilize and asymptotically eliminate the vibrations of the flexible-links that are naturally excited by the joints’ rotational motion. A first approach for the control of flexible-link robots is to consider the vibration modes as additional state variables and to develop stabilizing feedback controller for the extended state-space model of the flexible manipulator. To this end, one can use again (i) control based on global linearization methods, (ii) control based on approximate linearization methods, (iii) control based on Lyapunov methods. Another approach to the solution of the control problem of flexible manipulators is to treat the robot as a distributed parameter system and to apply control directly to the partial differential equations models that describe the motion of the flexible links. Again global asymptotic stability for this control approach can be demonstrated. On the other side, nonlinear filtering methods can be used for implementing state estimation-based feedback control through the measurement of a limited number of elements from the flexible robot’s state vector. In particular, the topics which are developed by the present chapter are as follows: (a) Inverse dynamics control of flexible-link robotic manipulators (b) sliding-mode control of flexible-link robotic manipulators.

Microrobots can be used in the manipulation and precise positioning of micro-objects, as well as in several microelectronics applications. Microrobotics is primarily concerned with control problems of micro electromechanical systems (MEMS). Specific problems that one encounters when developing microrobotic systems and MEMS is the imprecision about the micro-robot’s dynamic model and the inability to measure specific state vector elements in it. This in turn signifies that the design of feedback controllers for such systems has to be sufficiently robust to compensate for unmodelled dynamics or for parametric uncertainty. To this end one can consider either model-free control methods of proven stability (such as adaptive neurofuzzy control schemes), or model-based control methods capable of eliminating the effects of modelling errors, parametric inconsistency and external perturbations (such as H-infinity control). Moreover, one has to implement state estimation-based feedback control methods, making use of robust state observers, that will allow for estimation of the entire state vector of the microrobot or MEMS through the processing of measurements from a small number of sensors. In particular, the chapter treats the following topics: (a) Adaptive neurofuzzy control of micro-actuators, (b) Nonlinear optimal control of underactuated MEMS.

In complement to robotic manipulators, autonomous vehicles form the second large class of robotic systems. In this context, the autonomous or semi-autonomous navigation of unicycle-type and two-wheel vehicles, such as motorcycles, can be significantly improved through electronic control of the their stability properties. This will also allow for precise path following and for dexterous maneuvering. In this chapter, a nonlinear optimal control method is developed for solving the stabilization and path following problem of autonomous two-wheel vehicles. In the presented application examples either the kinematic or the joint kinematic-dynamic of the two-wheel vehicle undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control algorithm. The linearization takes place using Taylor series expansion and the computation of the Jacobian matrices of the system’s states-space model. For the approximately linearized model of the two-wheel vehicle an H-infinity feedback controller is designed. The computation of the feedback gain of the controller requires the repetitive solution of an algebraic Riccati equation, taking again place at each time-step of the control method. The concept of the control method is that at each time instant the system’s state vector is made to converge to the temporary equilibrium, while this equilibrium is shifted towards the reference trajectory. Thus, asymptotically the state vector of the two-wheel vehicle converges to the reference setpoints. Through Lyapunov stability analysis the global asymptotic stability properties of the control method are proven In particular, the chapter treats the following topics: (a) Nonlinear optimal control of robotic unicycles, (b) Flatness-based control of robotic unicycles, and (c) Nonlinear optimal control of autonomous two-wheeled vehicles such as motorcycles.

In the recent years there has been significant effort in the design of intelligent autonomous vehicles capable of operating in variable conditions. The precise modeling of the vehicles dynamics improves the efficiency of vehicles controllers in adverse cases, for example in high velocity, when performing abrupt maneuvers, under mass and loads changes or when moving on rough terrain. Using model-based control approaches it is possible to design a nonlinear controller that maintains the vehicle’s motion characteristics according to given specifications. When the vehicle’s dynamics is subject to modeling uncertainties or when there are unknown forces and torques exerted on the vehicle it is important to be in position to estimate in real-time disturbances and unknown dynamics so as to compensate for them. In this direction, estimation for the unknown dynamics of the vehicle and state estimation-based control schemes have been developed. Feedback control of robotic ground vehicles can be primarily based on (i) global linearization approaches, (ii) approximate linearization approaches and (iii) Lyapunov methods. The control is applied to (i) 4-wheel vehicles models, and (ii) articulated vehicles. At a second stage, to implement control under model uncertainty, estimation methods can be employed capable of identifying in real-time the vehicles’ dynamics. The outcome of the estimation procedure can be used by the aforementioned feedback controllers thus implementing indirect adaptive control schemes. Finally to implement control of the ground vehicles through the measurement of a small number of its state variables, elaborated nonlinear filtering approaches are developed. The topics treated by the chapter are: (a) Nonlinear optimal control of four-wheel autonomous ground vehicles (b) Nonlinear optimal control for an autonomous truck and trailer system (c) Nonlinear optimal control of four-wheel steering autonomous vehicles and (d) Flatness-based control of autonomous four-wheel ground vehicles.

The multi-DOF dynamic model of unmanned aerial vehicles (UAVs) is a highly nonlinear one and its control can be performed again with (i) global linearization control methods, (ii) local linearization control methods and (iii) Lyapunov analysis-based methods. In approach (i) the dynamic model of the UAV is transformed into an equivalent linear description through the application of a change of variables (diffeomorphisms). In (ii) the nonlinear model of the UAV is decomposed into local linear models for which linear feedback controllers are designed and next the aim is to select the feedback control gains so as to assure the global asymptotic stability of the control loop. In (iii) the objective is to define an energy function for the UAV (Lyapunov function) and to demonstrate that through suitable selection of the feedback control the first derivative of the energy function is always negative and thus the global stability of the control loop is assured. The latter approach is particularly suitable for model-free control of UAVs and takes the form of adaptive control methods. This chapter analyzes the aforementioned control approaches for UAVs and proves global asymptotic stability for all considered control approaches (i) to (iii). The robustness of the aforementioned control methods to model uncertainty and external perturbations is confirmed. Besides elaborated nonlinear filtering approaches are developed that allow for accurate estimation of the state vector of the UAVs through the processing of measurements coming from a limited number of sensors. In particular this chapter treats the following topics: (a) Control of UAVs based on global linearization methods, (b) Control of UAVs based on approximate linearization methods.

Autonomous navigation of unmanned surface vessels (USVs) (such as ships, hovercrafts, etc), is a significant topic, since it can find use in both security and defence tasks, as well as in maritime transportation. The problem of control and trajectory tracking for unmanned surface vessels (of the ship or hovercraft type) is non-trivial because the associated dynamic and kinematic models are complex nonlinear ones. A first problem that arises in controller design for unmanned surface vessels is that trajectory tracking has to be achieved despite modelling uncertainty and external perturbations and thus the control loop must exhibit sufficient robustness. Another problem that has to be dealt with is that the vessels model is often underactuated (the propulsion system consists of less actuators than the vessel’s degrees of freedom). The present chapter treats the problem of control of unmanned surface vessels. Solution to the associated control problem is provided through (i) global linearization methods, (ii) approximate linearization methods and (iii) Lyapunov methods. To solve the control problem for unmanned surface vessels without prior knowledge of the associated dynamic model, elaborated real-time estimation methods are developed. These allow for identifying the unknown dynamic model of the vessel and for implementing an indirect adaptive control scheme. Moreover, for the accurate localization of the vessel and for precise computation of its motion characteristics advanced (and precisely validated) nonlinear filtering and distributed filtering are applied. These enable to perform fusion of the measurements of heterogeneous sensors and of state estimates provided by individual distributed local filters. In particular, the chapter treats the following issues: (a) Nonlinear control and Kalman Filtering for a 3-DOF surface vessel, (b) Flatness-based control for the autonomous hovercraft (c) Nonlinear optimal control for autonomous navigation of unmanned surface vessels, and (d) validation of distributed Kalman Filtering for ship tracking applications.

The control of multi-DOF autonomous underwater vessels (AUVs) exhibits particular difficulties which are due to the complicated nonlinear model of the submersible vessels, the coupling between the systems control inputs and outputs, and the uncertainty about the values of their model’s parameters. Moreover, the AUVs’ dynamic model is subject to external perturbations which are caused by variable sea conditions and sea currents. Consequently, an efficient control scheme for AUVs should not only compensate for the nonlinearities of the associated dynamic model, but should also exhibit robustness to model parameter variations and to external disturbances. To this end, the present chapter provides results on robust control of AUVs, as well as on adaptive control of such submersible vessels. Thus the control problem for autonomous underwater vessels is treated with (i) global linearization methods (ii) approximate linearization methods and (iii) Lyapunov methods. The solution of the control problem requires a more elaborated procedure when the AUVs’ dynamic model is underactuated. which means that the number of actuators included in its propulsion system is less than the number of its degrees of freedom.The methods developed in this chapter treat also the case of underactuated AUVs. Moreover, advanced estimation methods are used to identify in real time the unknown dynamics of the underwater vessels or disturbance forces and torques that affect them. This allows for the implementation of indirect adaptive control schemes for the AUVs. Additionally, for the precise localization of the AUVs and their safe navigation elaborated nonlinear filtering methods are developed. These permit to solve problems of multi-sensor fusion as well as problems of decentralized state estimation with the use of spatially distributed nonlinear filters that track the AUVs motion. In particular the chapter treats the following topics: (a) Global linearization-based control of autonomous underwater vessels, (b) Flatness-based adaptive fuzzy control of autonomous submarines, and (c) Nonlinear optimal control of autonomous submarines.

Cooperating autonomous vehicles are analyzed. Distributed and coordinated control of autonomous vehicles (automatic ground vehicles, unmanned aerial vehicles, unmanned surface and underwater vessels) has received significant attention during the last years. In this chapter a solution is developed for the problem of distributed control of cooperating autonomous robots which chase a target. The distributed control aims at achieving the synchronized convergence of the autonomous vehicles towards the target and at maintaining the cohesion of the vehicle’s team, while also avoiding collisions between the individuals vehicles and collisions between them and obstacles in their motion plane. To estimate the motion characteristics of the target, distributed filtering is performed. It is shown that to treat the distributed control problem for the cooperating autonomous vehicles a Lyapunov theory-based method is introduced. Moreover, to treat the distributed filtering and state estimation in the multi-vehicle system, decentralized state estimation methods can be applied. The proposed distributed control and filtering method can be used for surveillance and security tasks executed by multi-robot systems. The method for coordinated control of autonomous vehicles is a generic one and thus applicable to various types of autonomous robots, such as automatic ground vehicles, unmanned aerial vehicles, unmanned surface vessels or autonomous underwater vessels. In particular, the chapter treats the following topics: (a) cooperating unmanned surface vessels and (b) Cooperating unmanned ground vehicles