MOTION CONTROL OF DENSE ROBOT COLONY USING THERMODYNAMICS A. D'Angelo Dept. of Mathematics and Computer Science University of Udine (Italy) ‏ T. Funato Dept. of Mechanical Engineering and Science Kyoto University (Japan) ‏ E. Pagello Dept. of Engineering and Computer Science University of Padua (Italy) ‏

Control Thousands of Robots Thermodynamics describes micro- dynamics from macro- view How to Control the Whole Robots! a sensor Every dust is Smart Dust Projects Microrobotics Projects Thousands of Robots inside

Our Purpose Construct a general method to control the diffusion/merging process of total system by reaction releasing of individual robots System can merge and maintain no control System only diffuses control the reaction

Thermodynamic Robot modeling Example [Thermal diffusion] ( H. Yuasa, Journal of SICE, 1999) ‏

Thermodynamic Robot modeling Example [Thermal Convection] Particle Heat Motion of robots Top robot receives packs and falls Down by the growth of the weight Robot starts transportation when the speed of the robots exceed certain value Robot The speed of Robot ( H. Yuasa, Journal of SICE, 1999) ‏ An application of thermal convection into transportation of Robot

Thermodynamical Metaphor A roboticle perspective applied to a dense robot colony

The expression of robot states by thermodynamic terms V: the area where occupied by robots P: pressure caused by the collision among robots Q: energy exchanged with the outer space U: total energy of the system diffusion : is positive merging : is negative W: work performed by changing the system volume The control of W is the purpose

The expression of robot states by thermodynamic terms Entropy S: Gibbs free energy G: System properties ( ) is described by individual robot property ( ) ‏ Macroscopic properties Microscopic property The first thermodynamic law

Gibbs Free Energy What is Gibbs Free Energy? The energy that is decided by the distribution of the particles ASSUME : The divergence proceeds acc. change of distribution Sum of heat flux H flows through its surface Gauss’s divergence theorem ( ) ‏ ( ) ‏

The diffusive force of each robots Fourier’s law of conduction The force acting individual robot: The heat equation for Generalized diffusing force Enthalpy

Discussion –connection with Roboticle Model The force acting individual robot: Dissipative part Conservative Part sensor system motor system Roboticle Model can be directly adopted to Thermodynamic Approach

Robot design by reaction releasing 1 diffusion : is positive merging : is negative : velocity on original trajectory : velocity by reaction is a positive frictional force Can the sign of dW be controlled by Fi?

Robot design by reaction releasing 2 Total energy of the robot system is conserved : adiabatic process System behavior can be controlled by manipulating the reaction Manipulate Diffusion/merging is controlled

Analogy with roboticle model and a prospect as an application System behavior can be controlled by designing sensor and motor relationship acc. above roboticle model equations Corresponds to the sensor/motor equations of roboticle model : velocity variation parallel to : velocity variation normal to

Under going work Robot Simulation

Network Thermodynamics A perspective of prof. Yuasa applied to roboticle model

What is the intelligent mobile robot? Motor Braitenberg Vehicles How to analyze? How to design? The robot that recognizes the environment and acts acc. the info. Sensor The Relationship generates the INTELLIGENCE Research of sensor/motor coordination

Roboticle Model and Network Thermodynamics : sensor system Current Roboticle Model : Sensor Motor Robot Behavior balance : motor system An expression used in Network Thermodynamics focuses on the connection among subsystems (H.Yuasa and T.Arai, IAS-7, 2002) ‏

Network Thermodynamics Basic Concept of Network Thermodynamics translate system into network of subsystem Local analysis Analysis of Connection Thermodynamics studies the effects of changes on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics (Wikipedia revised) ‏ What is thermodynamics? (G. Oster, A. Perelson, A. Kachalsky, Nature, 1971) ‏ (based on H.Yuasa, Journal on SCI, 1999) ‏

How are thermal elements expressed? Classical thermodynamics Heat: Q, Internal Energy: U Network thermodynamics Temperature: T Pressure: P The parameter that can be observed from Out

Flow and Effort –main valuables Flow f: the value passing through one point Flow Effort Effort e: the difference in the value of two points FieldFlow fEffort eint. of flow qint. of effort p electricityCurrent IVoltage vCharge q Magnetism  fluidbulk flow QPressure pVolume V Press. mom.  Mechanics (trans.) ‏ Force FVelocity vMomentum p Position x Mechanics (rot.) Torque  Angular velocity  Angular mom. H angular disp. 

Constraint Condition (KCL,KVL) ‏ FieldFlow fEffort eint. of flow qint. of effort p electricityCurrent IVoltage vCharge q Magnetism  fluidbulk flow QPressure pVolume V Press. mom.  Mechanics (trans.) ‏ Force FVelocity vMomentum p Position x Mechanics (rot.) Torque  Angular velocity  Angular mom. H angular disp.  Flows obey local conservative law KCL (Kirchhoff’s Current Law) ‏ Efforts are unique on every nodes KVL (Kirchhoff’s Voltage Law) ‏

Constraint Condition (KCL,KVL) ‏ Flows obey local conservative law KCL (Kirchhoff’s Current Law) ‏ Efforts are unique on every nodes KVL (Kirchhoff’s Voltage Law) ‏ Potential Energy : Kinematic Energy : Dissipative Energy : Energy

Analysis through Network Thermodynamic Approach Equations of Subsystems efpqefpq v (velocity) ‏ F (force) ‏ x (position) ‏ p (momentum) ‏ Spring Dumper Mass Flow and Effort

Analysis through Network Thermodynamic Approach KCL: Spring Dumper Mass KVL: Equations of the System can be calculated

Bond Graph A model of system based on the exchange of energy Construction of Bond Graph 1: put array showing the direction of energy 2: classify nodes Parallel junction 0-junction Serial junction 1-junction 3: delete the lines that energy is fixed (ex: ground) ‏

Representations by Bond Graph Electromagnetic System Representation by Bond graph model can be adopted in various field Locomotion Model

Future Prospect Bond Graph Expression Motor system Sensor system + Designing as Sensor/Motor Network

Future Prospect Structure based Robots Arrange through Bond Graphs Functional Structure Designing Functional Connection ? Analysis as Roboticle Model How functionality generates from structure?

Conclusions The thermodynamical metaphor seems suggesting a natural formulation of the relationship between the diffusion/merging of a dense robot colony and the behavior of each single robot Moreover, the Yuasa's perspective of Network Thermodynamics is the natural candidate to be applied to the roboticle colony model.