GMDH Application for autonomous mobile robot’s control system construction A.V. Tyryshkin, A.A. Andrakhanov, A.A. Orlov Tomsk State University of Control Systems and Radioelectronics E-mail: [email protected] Classification of existing autonomous robots Nearest analog – agricultural AMR “Lukas” Basic works on GMDH application to AMR control C.L. Philip Chen, A.D. McAulay Robot Kinematics Learning Computations Using Polynomial Neural Networks, 1991; C.L. Philip Chen, A.D. McAulay Robot Kinematics Computations Using GMDH Learning Strategy, 1991; F. Ahmed, C.L. Philip Chen An Efficient Obstacle Avoidance Scheme in Mobile Robot Path Planning using Polynomial Neural Networks, 1993; C.L. Philip Chen, F. Ahmed Polynomial Neural Networks Based Mobile Robot Path Planning, 1993; A.F. Foka, P.E. Trahanias Predictive Autonomous Robot Navigation, 2002; T. Kobayashi, K. Onji, J. Imae, G. Zhai Nonliner Control for Autonomous Underwater Vehicles Using Group Method of Data Handling, 2007; Part I Inductive approach to construction of AMR control systems Problems of AMR design Navigation Obstacle Recognition Autonomous Energy Supply Optimal Final Elements Control Technical State Diagnostics Objectives Execution Knowledge Gathering and Adaptation Generalized structure of AMR Objective aspects of AMR control system construction Utility Classification Realizability Taking into account Internal system parameters Appropriateness Forecasting Features of AMR obstacle recognition Lack of objects’ a priori information Objects to recognize are complex ill-conditioned systems with fuzzy characteristics Objects are characterized by high amount of difficultlymeasurable parameters It is necessary to take into account internal systems parameters for objects’ classification according to “obstacle/not obstacle” property, i.e. it isn’t possible to find out is this object obstacle or not without regard for system state. There is no necessity to perform full object identification, i.e. it isn’t necessary to answer a question “What object is this?” Part II Autonomous Cranberry Harvester Expected Engineering-and-economical Performance Nominal Average AMR speed: nom 4 km h Cranberry harvesting coverage: 2 m m Sharvest 4000 1.2m 4800 h h Relative density of harvested cranberry: 2 m Prel 4800 0.1kg 2 480 kg h h m Total weight of harvested cranberry per season: season kg 480 h 10 h day 30days 144000 kg Season income: $ 144000 kg 3.2USD kg 460800 USD Automated cranberry harvester Part III Simulation Results Object Recognition Data Sample Learning samples – 92; Training samples – 50. Values’ Ranges: Object Length L Є [0;20] м; Object Width w Є [0;20] м; Object Height h Є [0;20] м; Recognizing Modified Polynomial Neural Network F21 0.7512 0.0071 w h 0.0034 h 2 0.0062 w 2 0.0707 h 0.0855 w F31 0.7673 4.569 10 5 h t 2.157 10 7 t 2 0.0033 h 2 0.0004 t 0.0700 h F41 0.9573 9.4863 10 5 L t 2.500 10 7 t 2 0.0003 L2 0.0003 t 0.0500 L 7.9610 F 7.0944 F 26.054 F 11 .692 7.0954 F F 0.3786 F 7.0856 F 5.8304 F 20 .631 F 2.7575 0.2089 F L 0.0060 L 3.0244 F 0.2438 L 6.7788 F 6.290 0.3085 F L 0.0054 L 7.296 F 0.3526 L 14 .5629 F 1.3182 3.2282 F F 1.5832 F 0.0329 F 0.6605 F 3.3386 F F22 14 .805 11 .213 F21 F41 1.8830 F41 F42 F23 F13 F14 1 3 2 3 2 1 4 3 2 2 1 2 1 4 2 2 2 2 2 4 2 2 4 1 2 2 1 2 3 1 2 4 1 4 2 2 3 1 2 1 3 2 2 2 4 3 2 1 3 2 3 1 Objective Functions’ Data Sample Learning samples – 140; Training samples – 140. Values’ Ranges: Surface density of cranberry distribution ρcranberry Є [0;1] kg/m2; Cranberry harvesting efficiency η Є [20;75] %; Average AMR speed Vaverage Є [0;7] km/h; Nominal average AMR speed Vnomaverage Є [2;4] km/h; AMR engine fuel consumption per 100 km Pfuel Є [150;600] liters/100 km. Values’ laws of variation: Objective Functions Function of maximal cranberry harvest in preset time: F mcranberry , t 0.057 cranberry 2 Vaverage 11.86 cranberryVaverage t 0.012Vaverage t 2 Function of maximal cranberry harvest in minimal time: F mcranberry , t 6.684103 2 11.77 cranberryVaverage 0.693 cranberry Vaverage 2 t Function of maximal cranberry harvest with minimal fuel consumption: F mcranberry , m fuel 4.874103 cranberry 2 37.4 Vaverage 2 1 Pfuel 1257 cranberry 1 Pfuel Main Indices of Simulation Data 1) Obstacle recognition criterion values CR Percentage of Errors 0.055 12% 2) Objective Functions criterion values F(mcranberry,Δt) F(mcranberry,t) F(mcranberry, mfuel) CR BS CR BS CR BS 3.8e-4 9.8e-3 8.6e-3 0.9 1.8e-3 1.6 “Man should grant a maximal freedom to the computing machinery. Like a horseman having lost a way leave it to a discretion of his horse...” A.G. Ivakhnenko. “Long-term forecasting and complex system control”, Publ. “Технiка”, Kiev, 1975. – p. 8. Нахождение разделяющих областей в пространстве параметров распознавания Пространство параметров распознавания Область объектов-непрепятствий h L ` Область условно преодолимых препятствий Область объектов-препятствий Современные состояние разработок в области АПК Итерационный алгоритм МГУА с разделением обучения