| Sažetak (engleski) | Nowadays, the use of mobile robots has become increasingly important for many purposes: medical services, civil transport, domestic work, military, commercial cleaning, sales of consumer goods, agricultural and forestry work, browsing hard to reach and dangerous areas for human, digging ore, construction work, loading/unloading and manipulating materials, outer space and underwater research, space supervision, entertainment etc. New challenges in the field of mobile robotics include controlling a group of mobile robots in an efficient way. Inspiration is found in nature where many animal communities apply cooperative behaviour patterns to achieve a common goal. The most common arguments for the application of a group of mobile robots in comparison to only one mobile robot are increase in speed and accuracy and efficiency of performing tasks. A group of mobile robots is able to execute tasks impossible for a single mobile robot, e.g. transporting or repositioning large objects. Also, a group of mobile robots is more robust to failure than a single mobile robot (one mobile robot can take over the tasks of another mobile robot in case of failure). Since mobile robots can have a variety of roles, the same group of mobile robots can be employed for many different objectives, e.g. intelligent transport systems, areas coverage, cooperative transportation, logistics, etc. In order to achieve the benefits of multi-robot mobile systems it is necessary to solve additional problems in terms of control, which are not present in systems with a single mobile robot, e.g. communication between robots, distribution of tasks, assigning priorities, taking into account kinematic and dynamic constraints of all the mobile robots in the group to successfully plan feasible paths and trajectories for all of them, etc. A mobile robot is a mechanical system and as such is subject to motion equations that follow the laws of physics. Therefore, for each movement, in accordance with kinematic and dynamic constraints, there must be at least one set of input values that affect the motion. Kinematic constraints of mobile robots are the result of limitations in movement of drive wheels and drive configurations. Dynamic constraints of mobile robots refer to limiting the permitted velocity and acceleration, and they are caused by the actuator limitations. Motion control of mobile robots is a complex process. It includes working task planning, reference path and trajectory planning, and tracking the reference trajectory. The focus of this thesis is put on multi-robot land mobile systems and applications in intelligent traffic systems, areas coverage, cooperative transportation of large objects and coordination in the common working environment. All algorithms presented in this thesis are first tested in Matlab® and then experimentally validated on real robots. Experiments were performed using robot soccer platform at the Department of Control and Computer Engineering, Faculty of Electrical Engineering and Computing, University of Zagreb, which is ideal for testing various mobile robot algorithms. It consists of a team of five radio-controlled micro robots of size 0.075 m cubed with differential drive. The playground is of size 2.2×1.8 m. Above the centre of the playground, Basler a301fc IEEE-1394 Bayer digital colour camera with resolution of 656×494 pixels and with maximal frame rate of 80 fps is mounted perpendicular to the playground. The height of the camera to the playground is 2.40 m. A wide angle 6 mm lens is used. Although robot soccer platform is very practical for experiments with formations of mobile robots, it has some technical limitations: (i) relatively large noise in the measured position and velocity of the robot; (ii) delay in the communication between the control computer and microprocessors of the mobile robots and (iii) delay in measurements due to vision (the time required to grab the image from the camera and the time required for image processing). Efficient motion of mobile robots (vehicles) in a convoy formation is very important in transportation of people and goods. The key research problem is ensuring the string stability. In the background of this study are traffic safety and adaptive cruise control system in modern vehicles. The adaptive cruise control system primarily aims to reduce the driver’s effort, which is achieved by controlling the velocity of vehicle according to a predefined control law. Typically, sensors such as radar and lidar are used to measure the relative distance and relative velocity between vehicles. The working principle of adaptive cruise control system is based on these informations. String stability refers to the stability of a series of ''interconnected'' vehicles. The attribute ''interconnected'' does not indicate the physical connection of the vehicles but vehicles moving in a convoy formation where every vehicle in the convoy follows the preceding vehicle at a safe distance. The behaviour of each vehicle in the convoy must be such that the oscillatory behaviour due to a change of velocity of the leading vehicle of the convoy does not increase towards the end of the convoy. Otherwise, unstable convoy may cause collisions between vehicles. In this thesis, a deterministic microscopic full velocity difference model is considered. In the case where the values of model parameters do not meet the requirement of string stability, full velocity difference model should be expanded with additional control signals in order to satisfy string stability. Two additional control signals are based on the difference of the current and the delayed (in a defined time in the past) relative distance between the vehicle, and the difference of the current and the delayed vehicle velocity. The proposed method for achieving string stability is based on the delayed-feedback control. The delayed-feedback control is one of the feasible methods of controlling unstable and chaotic motions. The string stability has been examined by ∞–norm of transfer function of distance between vehicles. The stability of the transfer function is examined using a delay-independent stability criterion, which significantly simplifies the stability test, since characteristic equation of transfer function is transcendental and has infinite number of roots. It should be noted that the adaptive cruise control system is studied in one-dimensional space, e.g. vehicles in the convoy moving on an infinitely long straight road. Using formations of mobile robots, it is possible to significantly increase efficiency of numerous tasks such as areas coverage or cooperative transportation of large objects. However, achieving minimal time of executing tasks is a very challenging problem. The formation of mobile robots observed in this study is most similar to the formation with a leading mobile robot, but instead of a leading mobile robot the reference point of the formation and its reference path are defined. The formation of mobile robots is defined in the curved coordinate system so mobile robots maintain distance in relation to a reference point formation in this coordinate system. The curvature of the coordinate system is actually instantaneous centre of curvature of the formation’s reference trajectory. This results in changing the formation shape during cornering. This has implications in possible applications. For example, a square formation of mobile robots cannot handle rectangular solid object as it moves in curved path. The dynamic model of the mobile robot takes into account intrinsic constraints originating from the robot actuator limits and extrinsic constraints resulting from the limited adhesion force between ground and wheels of the mobile robot such as wheel slip and tip over of the mobile robot. Both types of constraints are important for planning at high velocities. The problem of planning reference time-optimal trajectory for a formation of mobile robot is solved by decoupled approach which could be defined as a problem of planning reference time-optimal trajectories after predefined smooth G2 continuous path of the reference point of formation. First, a path of formation of mobile robots in workspace is found, and then a velocity profile in accordance with the specified criteria and dynamic constraints of mobile robots is calculated. It is assumed that the path of each mobile robot in the formation is feasible and that kinematic constraints of the mobile robot on the path are satisfied. G2 continuous path provides the ability to pass the mobile robot trajectory with a non-zero velocity, thus enabling fast movement of the mobile robot without stopping. G2 path consists of straight lines and clothoids. Planning reference time-optimal trajectory for the formation of mobile robots is based on the optimal time-scaling algorithm providing that formation always moves at its maximum or minimum accelerations. This means that at least one mobile robot of the formation moves at its maximum or minimum accelerations. Emphasis is placed on static formations of mobile robots. Also, one example of dynamic formation of the mobile robots was shown. When multiple mobile robots independently perform tasks in the same workspace, the key problem is the planning collision free coordinated motion of multiple mobile robots sharing the same workspace. This problem is solved using the decoupled approach. First step is to plan individual path of each mobile robot, e.g. predefined path, using methods for planning paths for individual mobile robots in workspace with static obstacles. Second step is to plan a velocity profile for each mobile robot on its predefined path, e.g. predefined trajectory. Third step is to modify predefined trajectory for each mobile robot making sure that collisions between mobile robots in the workspace are avoided. To successfully coordinate motion of multiple mobile robots, a common approach is to assign priority level to each of them. A mobile robot with highest priority takes into account only static obstacles while other mobile robots have to take into account also dynamic obstacles, which are mobile robots with higher priorities. Dynamic obstacles avoidance is based on avoiding time-obstacles in a collision map. Time-obstacles are constructed based on the time mobile robots would spend in possible area of collision. A lower priority mobile robot efficiently avoids time-obstacles, e.g. mobile robot with higher priority level, by inserting a calculated start-up delay time to its predefined trajectory along the predefined path. By applying the same principle to all lower priority robots, a collision free motion coordination of multiple mobile robots can be achieved. It should be noted that the predefined paths of mobile robots do not change during their movements. The change is only in the allocation of time of motion of mobile robots on their predefined paths. A proposed method is computationally fast and intuitive and ensures that always only one mobile robot can be in the possible area of collision. The input of the trajectory tracking algorithm is a feasible planned trajectory, where feasibility refers to the ability of a mobile robot to actually track the planned trajectory. This means that the planned trajectory respects kinematic and dynamic constraints of the mobile robot. The trajectory tracking algorithm is needed because in reality there are many sources of potential errors such as imperfections of a mobile robot model or external disturbances like uneven ground, delayed command control, an imperfect measurement of the state of mobile robots and so on. In this thesis, it is proposed a trajectory tracking algorithm with constant gains for nonholonomic mobile robot with differential drive, which is based on kinematic model of mobile robot, nonlinear dynamics of the tracking error and Lyapunov stability theory. The scientific contributions of the thesis are: 1. Algorithm for mobile robot control in the formation of a convoy that ensures string stability using the delayed-feedback control, based on the difference between current and delayed distance between mobile robots and the difference between current and delayed velocity of a mobile robot. 2. Algorithm for planning smooth time optimal trajectory for a formation of mobile robots with kinematic and dynamic constraints on predefined paths. 3. Algorithm for planning of collision free motion coordination of multiple mobile robots sharing the same workspace on predefined paths assigning initial delay time for predefined trajectories of mobile robots. 4. Algorithm for trajectory tracking for mobile robots with kinematic and dynamic constraints based on Lyapunov stability theory. |
