Generalized predictive control (GPC)-type control algorithms traditionally derived in the polynomial domain are derived in this paper in the state-space domain, but following the polynomial approach due to Clarke et al. (1987). Relations between the polynomial and state-space parameters are presented. Some possible state-space representations which were used earlier in different publications are discussed. The problem of deriving the GPC algorithm in the state-space domain is solved for the unrestricted case as well as for the case of restricted control and output horizons. Some properties of the state estimate for this problem are presented; in particular, two methods of Kalman filtering—optimal and asymptotic—are proposed. The solution is valid for any possible (minimal or non-minimal) state-space representation. Another approach to this problem is by the ‘dynamic programming method’ and solving the Riccati equation (Bitmead et al. 1990). This approach is also presented in this paper but the method differs from this earlier work and does not require extending the state dimension. Ultimately, certain features of the state-space approach are discussed, such as (a) the opportunity for straightforward analysis of the transient states produced by switching on the regulator, by changing the set-point or by changing the regulator parameters; (b) easy extension to the multidimensional case; and (c) the possibility of introducing nonlinearities into the model

The paper presents and discusses a system (xDriver) which uses an Intelligent System of Decision-making (ISD) for the task of car driving. The principal subject is the implementation, simulation and testing of the ISD system described earlier in our publications (Kowalczuk and Czubenko in artificial intelligence and soft computing lecture notes in computer science, lecture notes in artificial intelligence, Springer, Berlin, 2010, 2010, In Int J Appl Math Comput Sci 21(4):621–635, 2011, In Pomiary Autom Robot 2(17):60–5, 2013) for the task of autonomous driving. The design of the whole ISD system is a result of a thorough modelling of human psychology based on an extensive literature study. Concepts somehow similar to the ISD system can be found in the literature (Muhlestein in Cognit Comput 5(1):99–105, 2012; Wiggins in Cognit Comput 4(3):306–319, 2012), but there are no reports of a system which would model the human psychology for the purpose of autonomously driving a car. The paper describes assumptions for simulation, the set of needs and reactions (characterizing the ISD system), the road model and the vehicle model, as well as presents some results of simulation. It proves that the xDriver system may behave on the road as a very inexperienced driver.

Collaborative robots cooperate with humans to assist them in undertaking simple-to-complex tasks in several fields, including industry, education, agriculture, healthcare services, security, and space exploration. These robots play a vital role in the revolution of Industry 4.0, which defines new standards of manufacturing and the organization of products in the industry. Incorporating collaborative robots in the workspace improves efficiency, but it also introduces several safety risks. Effective safety measures then become indispensable to ensure safe and robust interaction. This paper presents the review of low-level control methodologies of a collaborative robot to assess the current status of human–robot collaboration over the last decade. First, we discuss the classification of human–robot collaboration, architectures of systems and the complex requirements on control strategies. The most commonly used control approaches were presented and discussed. Several methods of control, reported in industrial applications, are elaborated upon with a prime focus on HR-collaborative assembly operations. Since the physical HRC is a critical control problem for the co-manipulation task, this article identifies key control challenges such as the prediction of human intentions, safety, and human-caused disturbances in motion synchronization; the proposed solutions were analyzed afterwards. The discussion at the end of the paper summarizes the features of the control systems that should be incorporated within the systematic framework to allow the execution of a robotic task from global task planning to low-level control implementation for safe and robust interactions.