دقت دینامیکی مکانیزم های روباتیک. قسمت 1: تجزیه و تحلیل حساسیت پارامتری

The paper is organized in two parts. Part 1 treats the problem of robot dynamic accuracy which has been scarcely elaborated in the literature. In this paper the error model of control by means of local feedback loops is given, which represents the initial research results in that field (N. Vešović, M. Vukobratović, Mech. Mach. Theory 29 (1994) 415–425). In this paper the error model of tracking trajectories using a dynamic control law, was developed and presented in detail. By using the inverse dynamics method (IDM) a control law was formed, into which the robot dynamics model was included and the sensitivity functions, which have served as the basis for the analysis of the variations influence on the dynamic robot parameters of the trajectory tracking accuracy were given.

Low accuracy is still one of the important obstacles to a wider utilization of robots in industry and, especially, a considerable impediment to a more extensive use of advanced robot programming techniques which incorporate off-line simulation and CAD-based systems. The definition of the robot accuracy is usually related to robot positioning, so that the accuracy is defined as a measure of robot ability to attain a required position with respect to a fixed absolute reference coordinate frame. Such a definition is easily extended to trajectory tracking. Then, accuracy can be defined as a measure of robot ability to track the prescribed trajectory with respect to the absolute coordinate frame. Robot accuracy is correlated with repeatability, which is a measure of robot ability to return to a previously reached and memorized position (or ability to track the memorized trajectory repeatedly). Although they express different things, robot accuracy and repeatability are sometimes intermixed: it is not uncommon that robot manufacturers state the value of the repeatability in the performance data sheets as the robot accuracy. Obviously, it is desirable that both accuracy and repeatability reach high standards. However, due to the fact that the absolute positioning accuracy is frequently greater than the repeatability by an order-of-magnitude, low accuracy of a robot is often regarded as a more serious problem, because it practically restricts such robot to the applications which can be satisfactorily programmed by ‘teaching by showing’ methods. Robot accuracy is influenced by a number of factors. Kochekali et al. [2] classify them into six categories: environmental (for example, temperature changes), parametric (variation of kinematic parameters, influence of dynamic parameters, friction and other nonlinearities, including hysteresis and backlash), measurement (resolution and nonlinearity of joint position sensors), computational (computer round-off and steady-state servo errors), and application (installation errors and workpiece position and geometry errors). Analysis of their influence and its elimination is a subject of intensive research aimed at the improvement of both accuracy and repeatability. Robots employ position sensors to obtain information on their current position. The position sensors can be external or internal. The external sensors are capable of giving the position and orientation of the robot gripper with respect to some absolute coordinate frame directly. However, such sensors are rarely applied because of their high cost and technical problems linked with their installation. On the other side, internal position sensors render the position of internal coordinates (joint displacements) of the robot. Position and orientation of the gripper are then calculated a posteriori, using the robot kinematic model. Thus, a difference can be made between the ‘internal’ and ‘external’ accuracy. Internal accuracy is the accuracy of attaining the prescribed set actuator position (or the accuracy of tracking the prescribed trajectory given in joint coordinates). Important factors influencing the internal positioning accuracy are steady-state servosystem errors, nonlinearities in the transmission from the actuator drive to the actuator output shaft, and imprecisely known gravitational moments loading the actuators. By a suitable selection of the servosystem, the influence of the steady-state error and load can be practically eliminated. Influence of deformation and backlashes in the transmission can be eliminated by measuring the position on the output actuator shaft, although such a solution is rarely encountered in industrial robots due to high price. Industrial robots usually exhibit large external positioning errors compared to the internal ones. Important sources of the difference between the internal and the external accuracy are off-sets between zero-reference readings of position sensors with respect to the actual zero positions of adjacent links, deviations of kinematic parameters from nominal values, and link deformations due to static load [1,3]. These factors contribute to the inaccuracy in mapping of the internal coordinates into the external ones, i.e. they influence the accuracy of the kinematic robot model that can be spoken as the ‘kinematic accuracy’ [4,5]. When considering the case of trajectory tracking, new factors, influencing primarily the internal trajectory tracking accuracy, appear. An important source of the internal tracking inaccuracy is the imprecise knowledge of the dynamic robot model: inertia parameters of the robot links and the workpiece held by the robot, actuator parameters, and deformation of the mechanism links caused by dynamic forces. By separating the mechanism dynamics and actuator parameters, that influence the internal trajectory tracking accuracy, one can speak about the ‘dynamic accuracy’, i.e. the accuracy of the dynamic robot model [3]. It has be emphasized that the accurate knowledge of dynamic parameters is of importance only when a high-quality tracking of fast trajectories is demanded, and this is more and more the case in robotic practice today. However, the assessment of the inaccuracy in dynamic parameters is an important factor in evaluating the quality of robust control strategies. Namely, the degree of influence of the accuracy of the dynamic robot model on the tracking accuracy depends on both the mechanism structure and the applied control algorithm. In the text to follow we shall consider the dynamic accuracy only. There exist several methods, in the scope of which the problem of manipulation robots accuracy is solved by using various control laws. Various control systems are introduced enabling good quality of system functioning under the action of significant uncertainties in the system itself and the working environment, hereby enabling the compensation of the influences of large irregularities during system work. The goal of the synthesis of intelligent control systems is similar to the case of conventional adaptive control algorithms. Similarity lies in the fact that the knowledge about the system is acquired directly during system operation by means of the learning processes, and the difference is that with intelligent control systems the uncertainty degree can be reasonably higher than that which can be tolerated in the case of adaptive control algorithms. Working requirements, set in advance, demand supplementary functions of the control system, as a perception of the working environment, associative reasoning under the action of uncertainty, learning, knowledge generalization and using experience, decision making process on several levels, etc. Intelligent control is a new discipline, representing the upgrade of the conventional systems control theory, because apart from the algorithmic-numeric control methods, it also uses the symbolic methods in the course of decision making processes, which were developed in the field of automata theory, operational research and notably, artificial intelligence. The directions of problem solving by means of very precise robots realization belongs to another group. Such robots are specific in the sense that their mechanical configuration is simpler, but that means they are more capable of producing higher accuracy in trajectory tracking. Such an approach to solving the accuracy problem is limited by several reasons. Technological possibilities to produce precise robot parts are among the most significant. Avoiding the gravitational loading influence of some of the precise manipulators, limits this kind of robot to practically the same SCARA configuration and low carrying capacity. In yet another group are the methods which model the causes of the external and internal inaccuracies of a robot and analyze the influence of the deviations of the real values of the model parameters from the nominal onto the accuracy of robot trajectory tracking. In that sense, this paper treats the manipulation robots dynamic accuracy based on the general sensitivity theory [6]. By means of the analysis of dynamic parameters deviations, the mathematical model is formed, based on which, in a qualitative and quantitative way, the intensity of the influence onto the robot accuracy can be evaluated. The sensitivity analysis is based on knowing the sensitivity functions. Generating these functions depends to a high degree on which control law has been adopted for the realizations of the trajectory tracking task. In each concrete case of the chosen control laws the method for obtaining the sensitivity function has to be elaborated. The sensitivity model is obtained by differentiating the system equations with respect to the chosen parameter, the influence of which is being analyzed. Each cause (deviation of the dynamic parameter from its nominal value) is modelled and analyzed separately. Due to the fact that the inaccuracy reasons are numerous and that it is not always possible to point to the dominant reason, the sensitivity models obtained by this method cannot be used directly for improving the trajectory tracking accuracy of the given robot. These methods are by their nature analytical and start from the assumption that the dynamic parameters deviate from their nominal values, i.e. that they are not sufficiently precisely known. Results of these analyses render a better insight into the possible causes of robot inaccuracy and, in that way, can be helpful in the design and manufacture of robots, whereby the causes of inaccuracy would be eliminated or made smaller. This method can point to the parameters, variation of which is of the greatest influence onto the trajectory tracking accuracy, so that they are to be identified with special attention.

This paper fills in a certain way, the gap in the field of robotic mechanisms dynamic accuracy, which is a very important issue of contemporary high-seed operation robots. The basic idea of the paper is to arrive, based on the analysis of the robot mechanism and driving unit dynamic parameters sensitivity, to some reliable conclusion about the rank of the relevant parameters sensitivity, in order to acquire a reliable basis for the design of the mechanical and control part of the robotic system, from the standpoint of their improved dynamic accuracy. For that reason characteristic feedback types were considered, notably the control feedback based on the complete dynamic model of the robotic mechanism.