Krzysztof Kozlowski

Fixed point transformations-based approach in adaptive control of smooth systems

The mathematical foundations of the modern Soft Computing (SC) techniques go back to Kolmogorov’s approximation theorem stating that each multi-variable continuous function on a compact domain can be approximated with arbitrary accuracy by the composition of single-variable continuous functions [1]. Since the late eighties several authors have proved that different types of neural networks possess the universal approximation property (e.g. [2]). Similar results have been published since the early nineties in fuzzy theory claiming that different fuzzy reasoning methods are related to universal approximators (e.g. in [3]). Due to the fact that Kolmogorov’s theorem aims at the approximation of the very wide class of continuous functions, the functions to be constructed are often very complicated and highly non-smooth, therefore their construction is difficult. As is well known, continuity allows very extreme behavior even in the case of single-variable functions. The first example of a function that is everywhere continuous but nowhere differentiable was given by Weierstras in 1872 [4]. At that time mathematicians believed that such functions are only rare extreme examples, but nowadays it has become clear that the great majority of the continuous functions have extreme properties. The seemingly antagonistic contradiction between the complicated nature of the universal approximators and their successful practical applications makes one arrive at the conclusion that if we restrict our models to the far better behaving “everywhere differentiable” functions, these problems ab ovo can be evaded or at least reduced.

Practical Stabilization of a Skid-steering Mobile Robot - A Kinematic-based Approach

This paper presents kinematic control problem of skid-steering mobile robot using practical smooth and time-varying stabilizer. The stability result is proved using Lyapunov analysis and takes into account both input signal saturation and uncertainty of kinematics. In order to ensure stable motion of the robot the condition of permissible velocities is formulated according to dynamic model and wheel-surface interaction. Theoretical considerations are illustrated by simulation results

Artificial potential based control for a large scale formation of mobile robots

This work presents control method based on a set of artificial potential functions. The kind of used artificial potential depends on particular objective: avoiding collisions between robots and keeping them in the ordered formation, executing task by the formation (e.g. moving formation into desired position), building formation and avoiding collisions with obstacles. In this paper we expand existing framework proposing attraction area potential function, which allows building formation and repulsion potential function, which allows avoiding collisions with obstacles. Main advantage of presented approach is that it is easy scalable because control is based on general rule that determines behaviour of all robots. Presented solutions are illustrated with simulation results.

Trajectory tracking of underactuated skid-steering robot

This paper considers problem of approximation of admissible trajectory for skid-steering mobile robot at kinematic level. Nonholonomic constraints at kinematic and dynamic level are taken into account. The trajectory tracking control problem is solved using practical stabilizer using tunable oscillator with novel method of tuning. The stability result is proved using Lyapunov analysis and takes into account uncertainty of kinematics. In order to ensure stable motion of the robot the scaling method is used. Theoretical considerations are illustrated by simulation results.

Feedback control framework for car-like robots using the unicycle controllers

The paper introduces a novel general feedback control framework, which allows applying the motion controllers originally dedicated for the unicycle model to the motion task realization for the car-like kinematics. The concept is formulated for two practically meaningful motorizations: with a front-wheel driven and with a rear-wheel driven. All the three possible steering angle domains for car-like robots-limited and unlimited ones-are treated. Description of the method is complemented by the formal stability analysis of the closed-loop error dynamics. The effectiveness of the method and its limitations have been illustrated by numerous simulations conducted for the three main control tasks, namely, for trajectory tracking, path following, and set-point regulation.

Lifelong education in robotics and mechatronics

Livelong education in electro-mechanical industry is increasingly important as it allows practicing engineers and technicians to gain the knowledge necessary to cope with the fast development and consequently with higher demands on their workplaces. This paper addresses different aspects of development and execution of such industrial training. Concrete solutions and results are presented including: (1) extensive international knowledge needs analysis in electro-mechanical sector, (2) e-learning solutions for industry including learning management systems and application of remote working stations/experiments for practical part of the training and (3) examples of the training modules from robotics developed for industry. Applied solutions and education methodology is evaluated by feedback obtained from the training participants. Based on a gained experience a long-term perspective and possible further development direction of modern industrial education is also addressed.

Motion planning and feedback control for a unicycle in a way point following task: The VFO approach

Motion planning and feedback control for a unicycle in a way point following task: The VFO approach This paper is devoted to the way point following motion task of a unicycle where the motion planning and the closed-loop motion realization stage are considered. The way point following task is determined by the user-defined sequence of way-points which have to be passed by the unicycle with the assumed finite precision. This sequence will take the vehicle from the initial state to the target state in finite time. The motion planning strategy proposed in the paper does not involve any interpolation of way-points leading to simplified task description and its subsequent realization. The motion planning as well as the motion realization stage are based on the Vector-Field-Orientation (VFO) approach applied here to a new task. The unique features of the resultant VFO control system, namely, predictable vehicle transients, fast error convergence, vehicle directing effect together with very simple controller parametric synthesis, may prove to be useful in practically motivated motion tasks.

A backstepping approach to control a nonholonomic mobile robot

A trajectory tracking control problem for a nonholonomic mobile robot by making use of a kinematic oscillator has been solved. Firstly, a time varying oscillator is examined to control the nonholonomic mobile robot based only its kinematics. Secondly, a backstepping procedure is proposed to include robot dynamics and the servo loop. It is shown that overall multilevel controller is asymptotically globally stable to a small error different from zero. A wide range of simulation results are presented which illustrate the behaviour of the controller with respect to tuning its parameters. Some preliminary experiments are reported too.

A novel approach to the Model Reference Adaptive Control of MIMO systems

The “Model Reference Adaptive Control (MRAC)” is a popular approach from the early nineties to our days. Its basic idea is the application of proper feedback that makes the behavior of the controlled system identical to that of the “reference model” that normally is simple enough to control. The idea has many particular variants with the common feature that they are designed by the use of Lyapunovs 2nd (“direct”) method that normally applies a quadratic Lyapunov function constructed of the tracking error and further additional terms. Though this approach normally guarantees global asymptotic stability, its use can entail complicated tuning that may have disadvantages whenever very fast applications are needed. In this paper an alternative problem tackling, the application of “Robust Fixed Point Transformations (RFPT)” in the MRAC technique is recommended. This approach applies strongly saturated, multiplicative nonlinear terms causing a kind of “deformation” of the input of the available imprecise system model. Instead parameter tuning that is typical in the traditional MRAC it operates with a simple convergence guaranteed only within a local basin of attraction. This technique can well compensate the simultaneous consequences of modeling errors and external disturbances that normally can “fob” the more traditional, tuning based approaches. As a potential application paradigm the novel MRAC control of a “cart - beam - hamper” system is considered. The conclusions of the paper are illustrated by simulation results.

Design of a planar high precision motion stage

Over the last 50 years one has been able to observe enormous enhancement in positioning and measuring accuracy. The main portion of this enhancement is the result of improved knowledge about high precision machine design. A fundamental principle was recognized by Professor Abbe already in the 1890s about the aligment of the displacement measuring system with the distance to be measured. Another fundamental principle is the separation of the structural and measuring functions in a machine. As mechanical accuracy is costly, unlike repeatability, software techniques were used from the beginning to compensate for the systematic errors in order to keep manufacturing costs low.