Another interesting approach is using hindsight optimization, where the system uses a Markov Decision Process (MDP), to determine the most probable goal from user inputs and move more efficiently towards the goal based on the input values. In a paper by S. Javdani et al.  they approximate the optimal action using QMDPs which are a combination of MDPs and Partially observable Markov Decision Processes (POMDPs). The experimental setup consists of known object positions in task space and assumes each object can have any grasp pose. The system uses the user input to estimate the best possible path to follow and also which object is desired by the user to be grasped using directional guidance from user. It can be better understood from the illustration extracted from the paper shown in figure 2.5. We can see initially all object have a similar probability of being the final goal object to be grasped, but as human input is given the robot can better estimate which object is to be grasped and proceed with the task. This implementation can be advantageous in situations of having to decide between multiple goals to choose from.
For understanding the Kinematics of car like mobile robot first we must know the type of wheels we are using in our case and also the constrained applied due to it. In common case disk type wheels are used for a carlike wheeled mobile robot. In case of simulation, a car like model can be designed using simple geometric and trigonometric concept for more understanding please refer . Many control approaches have been put forward to solving the motion control problem such game theory, modelpredictivecontrol and so on. We have use Fuzzy logic (type-2) in our case. Seong-Gon Kong in  presented a work in type1 fuzzy logic controller having two input and one output state variable. x coordinate and vehicle orientation where the input to the controller whereas the output is the vehicle steering angle. The rule base used is a very common rule base used for mobile robot case, nearly similar kind of rule base is given in -.We have designed a new rule base having 25 rules for our case. Many times it is seen that the data that is used to develop the rules for a fuzzy system are uncertain. Due to the uncertainty, like an uncertainty in collection of information for a same case by different people, it becomes tough to decide what the exact value of membership function is. The overall structure of fuzzy sets in a fuzzy system is to allow the handling and modeling of much of uncertainty using type-1 fuzzy sets. But Type-1 fuzzy logic systems are not able to completely handle the linguistic or numerical uncertainties . In such a case we need another kind of fuzzy set for a fuzzy system called as type 2 fuzzy set. A type-2 fuzzy logic system or controller uses notation that are very much similar to that are used in a type-1 fuzzy logic controller such as membership functions, fuzzy rules, t-norms operations, fuzzification, inference, defuzzification. The only difference is that addition of type reduction process before defuzzification. The basic ideas of IT2-FL in Matlab is explained by Dongrui Wu in  whereas Hani hagras  explains the theoretical concept of type2 FLS in simple language. The paper is arranged as follow Section II gives kinematic information of mobile robot along with kinematic constraints, also telling why we are having these constraint and how our mobile robot move in its environment, section III is focused on our leader-follower formation problem. Section IV gives the theoretical concept of Type2 fuzzy logic along with the proposed controller. Section V shows the simulation results whereas Section VI tells the conclusion.
Despite the fact that the model-based predictivecontrol is not a new control method, works dealing with model-based predictivecontrol and wheeled robots are few and scattered. The generalized predictivecontrol is used in  to solve the trajectory-tracking problem. Although, the control in this work acts only on the angular velocity and the linear velocity is supposed constant. A nonlinear model of wheeled mobilerobots is used for trajectory tracking in . The problem is solved using a neural network that considers unknown obstacles in the configuration space. There were also works using nonlinear model of robot and nonlinear modelpredictivecontrol as in  where the authors developed a state space representation of a nonlinear modelpredictivecontrol and they applied it to the problem of point stabilization and trajectory tracking.
configuration of the optimum potential field is automatically determined by genetic algorithm. Simulation experiments performed with three different obstacle configurations, and ten different routes, showed that the scheme reported has a good performance in environments with high obstacle densities, achieving a success rate of 93 per cent. Xin et al.  have proposed a method of global path planning based on neural network and genetic algorithm. They constructed the neural network model of environmental information in the workspace for a robot and used this model to establish the relationship between a collision avoidance path and the output of the model. Then the two- dimensional coding for the path via-points was converted to one-dimensional one and the fitness of both the collision avoidance path and the shortest distance are integrated into a fitness function. The simulation results showed that the proposed method is correct and effective. Wong et al.  proposed, a method based on Genetic Algorithms (GA) is to design a fuzzy system to control an omni-directional mobile robot so that it can move to any direction and spin at a rotating rate. In this method, an individual of the population in the GA-based method is used to automatically generate fuzzy sets of the premise and consequent parts of fuzzy system. A fitness function is proposed to guide the search procedure to select an appropriate parameter set of the fuzzy system such that the output of the fuzzy system can approach the output of data base established from the kinematics model of the three-wheeled mobile robot.
In chapter 2 are presented the dynamic models of VTOL UAV and di ff erential wheel robot. The VTOL UAV is suitable to model the multi-propeller UAV used in the project, and we propose a novel strategy to model this class of vehicles with a modular approach, where the UAV is seen as composition of payload and actuators modules. This will al- low to model general multi-propeller vehicles with non-standard configurations. About the differential wheel robot, the model used is a standard unicycle model to define the kinematic, which is often su ffi cient to build accurate models and control strategies. In chapter 3 we propose the control law for the two robots of interest. For the VTOL UAV we propose an hybrid control law with a cascade approach, where the continuous position controller is in cascade with the hybrid attitude controller. It allows to over- come a topological obstruction for continuous law on compact manifolds such as SO(3) for the attitude, and allows to robustly execute acrobatic maneuvers such as flips and attitude recovery, useful for the aerial deployment task of the project. About the di ff er- ential wheel robot, a vectored speed control is proposed, with saturation on the velocity input to represent the constraints on the actuator. The proposed control allows to reach a waypoint in a 2D plane starting from any initial configuration or to track a desired position trajectory.
The research documented here demonstrates that the RFNN and the HECNN are viable pattern analysis and control engines that contribute to the solution of a variety of problems. The theoretical development of the RFNN and HECNN, along with several proof-of-concept applications, is presented in detail. For the RFNN, we present a back-propagation model that is more general than standard textbook models because it also accomodates receptive fields and weight sharing. Also for the RFNN, we present a modified version of adaptive learning rates, called “shocking”, which reduces training time while maintaining stability. Due to its modularity, the RFNN allows the user to construct flexible, multi-layered, feed- forward architectures as well as add to and prune from an architecture even after training has begun. Architectures can be fully or partially connected, with or without receptive fields. The RFNN also permits the user to include previously learned features, called “analogies”, to further expedite the training process on new problems or whenever new classes are added. The large-scale pattern analysis problems presented here for the RFNN include: sonar pattern recognition and outdoor landmark recognition. Small-scale benchmark problems like the XOR and XOP (×, and +) problems are used to demonstrate the utility of the “shocking” model.
As a trial to move the robot through the given environment, fuzzy control concept has already proven to be worthwhile in both global and local path planning tasks for autonomous mobile objects. A set of linguistic fuzzy rules are developed to implement expert knowledge under various situations. Sensor signals are fed to the controller and the output provides motor control commands (e.g. turn left or right). Under the control of the proposed fuzzy logic-based model, the mobile robot can generate paths towards the target by integrating different preliminary robotic behaviours. The artificial life approach to evolutionary robotics is specifically designed to grow a neural structure with complex dynamical properties for path recognition of autonomous mobile robot. Neural networks are often used to enhance and optimize the outcome of fuzzy logic based system, e.g. by introducing a learning ability. This learning ability is achieved by presenting a training set of different examples to the network and using learning algorithm, which changes the weights (or the parameters of activation functions) in such a way that network will reproduce a correct output for the input values associated with nonlinearities.
represents the dynamic system modelling in various operating points. Each sub-model is a feedforward neural network trained with back-propagation algorithm. The output of these submodels is weighted with the help of a neural network with a base function to generate motion commands for the robot. The performance of the local neural network is compared to a multilayer perceptron network and a radial basis function as a parameter to measure performance, measuring takes the time it takes the robot to reach its goal or destination.
Hence the idea of developing a distributed system. The global system is decomposed into several subsystems. Each subsystem has a MPC controller which communicates with the others. Local control inputs are then locally computed and determined with the few information shared. For ins- tance, when a decentralized control scheme (where local control input are determined based on local measurements for instance) is needed, a distributed MPC is a better choice. For example, for water distribution systems, a centralized MPC is decomposed into a DMPC using a coordinator (e.g.
Li et al.  have designed and implemented an autonomous car‐like mobile robot (CLMR) control system, where the set up consists of the host computer, communication module, CLMR, and vision system. They have used fuzzy garage‐parking control (FGPC) and fuzzy parallel‐parking control (FPPC) to control the steering angle of the CLMR. Li et al.  have used the concepts of car maneuvers, fuzzy logic control (FLC), and sensor‐based behaviours to implement the human‐like driving skills by an autonomous car‐like mobile robot. They have used four kinds of FLCs: i) fuzzy wall‐following control, ii) fuzzy corner control, iii) fuzzy garage‐parking control, and iv) fuzzy parallel‐ parking control, which are synthesized to accomplish the autonomous fuzzy behaviour control (AFBC). They have presented computer simulation results to illustrate the effectiveness of their proposed control schemes and demonstrated the feasibility in practical car maneuvers. Baturone et al.  have described the design and implementation of a fuzzy control system for car‐like autonomous vehicle. They have addressed problem for diagonal parking in a constrained motion. Ohkita M. et al.  have controlled an autonomous mobile robot for the flush parking. They have used fuzzy rules those are derived from the modelling driving actions of a car. Zhao et al.  have developed and experimentally demonstrated a robust automatic parallel parking algorithm for parking in compact spaces. They have designed novel fuzzy logic controllers for each step of the maneuvering process. The controllers are first demonstrated by simulation using the kinematic model of a skid steering autonomous ground vehicle (AGV).
Navigation of multiple mobilerobotsusing neuro-fuzzy controller has been discussed in this paper. In neuro-fuzzy controller the output from the neural network is fed as an input to fuzzy controller and the final outputs from the fuzzy controller are used for motion control of robots. The inputs to the neural network are obtained from the robot sensors (such as left, front, right obstacle distances and the target angle). The neural network used consists of four layers and the back propagation algorithm is used to train the neural network. The output from the neural network is initial-steering-angle. Inputs to the fuzzy-controller are initial-steering-angle (the output from neural network) and left, front, right obstacle distances. The outputs from the fuzzy controller are the crisps values of left and right wheel velocity. From the left and right wheel velocity final-steering-angle of a robot is calculated. The neuro-fuzzy controller is used to avoid various shaped obstacles and to reach target. A Petri-net model has been developed and is used to take care of inter-robot-collision during multiple mobile robot navigation. A piece of software has been developed under windows environment to implement the neuro- fuzzy controller for robot navigation (appendix-1). Six real mobilerobots are built in the laboratory for navigational purpose (appendix-2) in reality. By using the above algorithm it is visualised that, multiple mobilerobots (up-to one thousand) can navigate successfully avoiding obstacles placed in the environment.
Typical examples of discrete event systems are flexible manufacturing systems, telecommunication networks, par- allel processing systems, traffic control systems, and logis- tic systems. The class of discrete event systems essentially consists of man-made systems that contain a finite number of resources (such as machines, communications channels, or processors) that are shared by several users (such as product types, information packets, or jobs) all of which contribute to the achievement of some common goal (the assembly of products, the end-to-end transmission of a set of information packets, or a parallel computation) . In general, models that describe the behavior of a discrete event system are nonlinear in conventional algebra. How- ever, there is a class of discrete event systems – the max- plus-linear discrete event systems – that can be described by a model that is “linear” in the max-plus algebra , , which has maximization and addition as its basic op- erations. The max-plus-linear discrete event systems can be characterized as the class of discrete event systems in which only synchronization and no concurrency or choice occurs. So typical examples are serial production lines, pro- duction systems with a fixed routing schedule, and railway
The ordinary motion control methods in robotics are comprised of two phases: 1) the motion planning phase  and 2) the trajectory following phase. In the biped robots, the motion planning (i.e. the gait generation) phase may be performed off-line or on-line . The offline gait generation cannot adapt to the environment changes like obstacles, which can reduce the robot’s abilities to walk. There are different methods for the on-line gait generation that can adapt to the environment. An on-line adaptive optimal gait pattern would facilitate best the biped robot motion control. Although consuming more efforts to reduce the error of tracking is the goal of lots of control problems, perfect joint trajectory tracking is not necessary in the biped motion control since the biped robot may have normal and acceptable walk even if there are some errors in the trajectory tracking of the joints. Thus, ordinary robot motion planning methods may not fit well to the biped robots. The Human walking approach is based on optimal algorithms, which use some goals and constraints to displace the body or the Center of Mass (CoM) from one point to another, while considering and predicting the environment changes, in order to decide adaptively to accomplish safe and without falling walk . A suitable way of imitating this behavior for motion control of the biped robot is to state the problem as a non- linear model based predictivecontrol [15-17]. With an appropriate objective function, while considering the state and the control signal constraints plus the physical constraints, it is possible to combine the gait pattern generation phase with the control phase and allowing the NMPC to decide about both the gait pattern and the control signals. In this approach, there are no trajectories to follow. Instead, the control signals are generated by the NMPC directly in such a way that the biped robot is able to walk. In addition to the advantages of the on-line gait generation, this method considers the biped dynamics, constraints of the control signals, the present and the future of the biped states, and the physical constraints in the robot to execute more optimal and practical walking.
(Camacho et al., 1998; Peña, 2002), although this strategy is considered heavy due to its computational effort in practice. The NMPC stability analysis with finite receding horizon has been studied in Mayne et al. (2000) and Fontes (2001). Recently, the qualities of predictivecontrol have been explored and applied in robotics, woks like Dongbing et al. (2006), Hedjar et al. (2005), Künhe et al. (2005) and Ramírez et al. (1999) show different approaches and strategies in MPC with good results for tracking control and regulation. This paper applies NMPC to dynamic model of mobile robot and makes an analysis by computes times for optimization algorithm so that to be able to implement the controller in experimental works.
LMPC is primarily developed for process control. There- fore its application in robot control has less been reported. The incipient interest in the applications of MPC dates back to the late 1970s. In 1978, Richalet et al. , pre- sented the ModelPredictive Heuristic Control (MPHC) method in which an impulse response model was used to predict the effect at the output of the future control ac- tions. Linear modelpredictivecontrol refers to a class of control algorithms that compute a manipulated variable pro- file by utilizing a linear process model to optimize a lin- ear or quadratic open-loop performance objective subject to linear constraints over a future time horizon. The first move of this open loop optimal manipulated variable pro- file is then implemented. This procedure is repeated at each control interval with the process measurements used to update the optimization problem. During 1980s, MPC quickly became popular particularly in chemical process industry due to the simplicity of the algorithm and to the use of the impulse or step response model, which is pre- ferred, as being more intuitive and requiring no previous information for its identification .
We validate our control algorithms by using physical omnidirectional mobilerobots, shown in Figure 3.1, later rebuilt, shown in Figure 3.5. The architecture utilizes a Pentium-M 2 GHz onboard PC with 1 GB RAM for the main processing unit. There are three Swedish wheels placed in such orientation that their axes of rotation point to- wards the center of the robot and there is an angle of 120 ◦ between them. Each wheel is driven by a 24-Volt Maxon DC motor of 60 Watt each with 18:1 gear ratio, and has the same distance L w from its center to the robot’s center of mass (point R in Figure 3.2). Figure 3.3 shows a photograph of the real hardware with the top view of the general three-wheeled omnidirectional mobile robot model. Optical encoders are mounted on each motor shaft to provide feedback for the motor speed controller. The control sys- tem consists of two loops: the outer loop is an external kinematic loop, while the inner loop is the low-level actuator velocity servo loops. In particular, the low-level motor speed feedback control is realized by a three-channel digital PID board (the TMC200 designed and built at AiS - Fraunhofer Autonomous Intelligent Systems Institute) with pulse-width modulation (PWM) output. The TMC200 board is interfaced through a se- rial RS232 link with an onboard PC. In the old structure designated for the RoboCup competition, there was an omnidirectional camera as a sole sensor, which was used for self localization within the RoboCup field, developed by Heinemann et al. . This self-localization algorithm was based on probabilistic Monte-Carlo localization (MCL). The vision system consisting of a Marlin F-046C camera and a hyperbolic mirror em- ployed on the mobile robot platform provides a 360 ◦ field of view. The Marlin F-046C has a resolution of 780x580 pixels and is able to capture and transmit 50 fps at a reduced resolution of 580x580 pixels in the 16 bit YUV4:2:2 format via the IEEE 1394a FireWire bus . In the new structure designated for robot service purposes, the sensory systems consist of six sonar sensors, one laser scanner, and one vision system. The overall system uses 24-Volt NiMH batteries.
In  an ANFIS-Controller was developed for the navigation of a mobile service robot with two differential wheels. It was trained to recognize and follow a line on the floor to its goal position. To realize this the desired motor speed values were predefined in a teacher vector. The fuzzy controller was then adapted in premise and consequence parameters of the rule base via supervised learning and could eventually lead the robot along the line. An approach for an obstacle avoidance controller is given in , where a two-wheeled robot should be able to move in a fixed area without colliding with the objects lying within. The parameters of the membership functions and the consequence part were adpated with supervised learning. The controller was tested in simulation and also experimentally. The authors in  focused on the adaption of the parameters in the membership functions. They predefined all parameters and set a perfect route to a goal position without colliding with an obstacle. This path was then used for adapting position and slope of the membership functions to "smooth the trajectory generated by the fuzzy logic model". The controller was employed sucessfully in a two wheeled, differential driven robot. To decrase the number of rules in one fuzzy controller the navigation algorithm in  is split up in a hierarchial system. Within this, different behaviours like e.g. "goto-target" or "turn-corner" are realized with respective neuro-fuzzy controllers. By doing this they could avoid having one big rule base to include all navigation orders.
of robust controls for stabilization of differential drive robots. This paper shows the success of dynamic feedback linearization approach in stabilizing the posture of robot via analytical proof and simulation results. Also, to verify the performance of the proposed control strategy, another control is designed for the comprehensive model. The performance and ease of tuning of the two controllers are compared. The results of simulations show that the dynamic feedback linearization based control has a smoother stabilization path and easier tuning process. Finally, the performance of the proposed controller is studied under parametric uncertainties. The results of the simulations show that the proposed control has a very good performance against uncertainties.
The y-alignment of the die has a large influence, specially in timing as can be seen in Figure 4.3d. A negative misalignment causes a different curvature at the start of the free bending stage as there is no contact with the tip of the die initially. The time at which the contact area starts to change and the time at which the contact with the die takes place both shift in positive direction with negative misalignment. Generally a negative alignment means less force needed to bend the flap. In the experimental force curves the peak in the force curve is generally seen wider, than in the FE-model. Therefore the choice is made to set the minimum y-alignment of the die to −0.01 mm.
together with tougher environmental regulations, rigorous safety codes and rapidly changing economic situations demand the need for more sophisticated process controllers. Modelpredictivecontrol (MPC) is an important branch of automatic control theory. MPC refers to a class of control algorithms in which a process model is used to predict and optimize the process performance. MPC has been widely applied in industry (Qin and Badgwell, 1997). The idea of MPC is to calculate a control function for the future time in order to force the controlled system response to reach the reference value. Therefore, the future reference values are to be known and the system behavior must be predictable by an appropriate model. The controller determines a manipulated variable profile that optimizes some open-loop performance objective over a finite horizon extending from the current time into the future. This manipulated variable profile is implemented until a plant measurement becomes available. Feedback is incorporated by using the measurement to update the optimization problem for the next time step. Figure 1 explains the basic idea of MPC showing how the past input-output information is used to predict the future process behavior at the current time and how this information is extended to future to track the desired setpoint trajectory. The notation y, u and T s refer process output, control action and