Vol.3, No 11, 2001 pp.285-294
UDC 517.93+519.713:007.52(045)
MATHEMATICAL MODELING AND CONTROL
OF REDUNDANT ROBOTIC MANIPULATORS
USING BIOLOGICAL ANALOG
Mihailo P. Lazarević
Faculty of Mechanical Engineering, University of Belgrade, 27 Marta 80, 11000 Belgrade, Yugoslavia, Fax: (381-11) 3370-364 Tel: (381-11) 3370 -760/ loc. 338
E-mail: lazarem@alfa.mas.bg.ac.yu
Abstract. In this paper it is considered problem of realization new mathematical models of redundant systems as well as control using suitable biological analog. The idea was to try to imitate human behavior and this is specially convenient for tasks which are similar to those characteristic for humans (e.g., assembling in industry, different jobs at home and in health service). If we consider speed, accuracy and stability of motion then the overall performance (taking into account all three of parameters) with machines is still far behind human reaching and grasping. Human arm movements are considered to be stable, fast and accurate due to properties of muscles, musculo-skeletal structures and hierarchical control. It was observed in the execution of functional motions that certain trajectories are preferred from the infinite number of options. Such behavior of organisms can be only explained by the existence of inherent optimization laws in self-organized systems governing the acquisition of motor skills. Existence of invariant features in the execution of functional motions points out that central nervous system (CNS) uses synergy [Bernstein,1967](i.e rule(s) that can be developed by the CNS based on some principles). The control of arm movement in humans relies very much on distributed usage of different joints, and inherent optimization of muscles which are active. Analysis of multijoint coordination in humans is an important source of information for synthesis of dynamic patterns in machines. In that way, model of redundant system is obtained using biomechanical principle - synergy i.e. introducing linear or nonlinear relations between independent parameters or their first derivatives which uniquely define redundant system. Moreover, one can introduced hypothetical control using joint actuator synergy approach as suggested [Bernstein, 1967] which imposes a specific constraint(s) on the control variables. Also, it can be applied biological concept called distributed positioning (DP) which is based on the inertial properties and actuation capabilities of joints of redundant system. The redundancy and DP concept [Potkonjak 1990] could be used for solving the trajectory that has problems with increased dynamic requirements. The concept of DP allows us to separate the smooth and accelerated components of required motions applying appropriate smoothing technique. The inverse kinematics of redundant robot has been solved at the coordination level via (DP) concept. Moreover, it is here proposed using other biological principles such as: principle of minimum interaction which takes a main role in hierarchical structure of control and self-adjusting principle, which allows efficiently realization of control based on iterative natural learning. Motor control is organized as a multilevel structure, is generally accepted. In assistive system involves man as the decision maker, a hierarchical control structure can be proposed with three levels from the left to right: -voluntary level, coordination level, actuator level. This imposes the system is decomposed into several sybsystems with strong coupling between subsystems. Explanation of previous can be understood using the principle of maximum autonomy or minimum information exchange [Tomović, Bellman, 1970]. According to this principle, the optimal solution is to delegate the execution of functional motions to the coordination level and local regulators once the task and the task parameters have been selected. Learning control for controlling dynamics systems, a class of tracking systems is applied where it is required to repeat a given task todesired precision. The common observation that human beings can learn perfect skills trough repeated trials motivations the idea of iterative learning control for systems performing repetitive tasks. Therefore, iterative learning control requires less a priori knowledge about the controlled system in the controller design phase and also less computational effort than many other kinds of control. For improving the properties of tracking is proposed appling biological analog - principle of self-adaptibility, [Grujuć,1989 ] which introduce local negative feedback on control with great amplifing.
MATEMATIČKO MODELIRANJE I UPRAVLJANJE REDUDOITNIM ROBOTIMA-MANIPULATORIMA KORIŠĆENJEM BIOLOŠKIH ANALOGA
U ovom radu razmatran je problem realizacije novih matematičkih modela redudantnih sistema kao i upravljanja korišćenjem pogodnih bioloških analogona. Ideja je bila u tome da se imitira ljudsko ponašanje i to je posebno značajno za zadatke koji su slični onim zadacima karakterističnim za ljude. Prvo, može se primeniti biološki koncept distribuiranog pozicioniranja (DP) koji je zasnovan na inercijalnim osobinama i aktuatorskim mogućnostima zglobova redudantnih sistema. Drugo, predloženo je korišćenje biološkog analogona - sinergije koja je posledica postojanja invarijantnih osobina u izvršavanju funkcionalnih kretanja. Na kraju predloženo je korišćenje drugih bioloških principa kao što su: princip minimuma interakcije koji ima važnu ulogu u hijerarhijskoj strukturi upravljanja i principa samopodešavanja, koji dozvoljava efikasnu realizaciju upravljanja koje je zasnovano na iterativnom prirodnom učenju.