Cálculo Fraccinario en Control y Robótica. Aplicaciones en Robótica Móvil

Transcripción

1 Cálculo Fraccinario en Control y Robótica. Aplicaciones en Robótica Móvil José Ignacio Suárez Marcelo Universidad de Extremadura Escuela de Ingeniería Industrial Badajoz (Spain) 5-26 de marzo de 2003

2 Indice de Contenidos Vehículos Autónomos Cálculo Fracional en Control de Vehículos

3 Vehículos Autónomos

4 ISAAC: El proyecto ISAAC Integración Sensorial para Ayudas Activas a la Conducción Objetivo: desarrollar ayudas activas a la conducción de vehículos, integrando información sensorial, sistemas de control, interfaces y comunicaciones inalámbricas Ayudas Activas: proporcionar advertencias al conductor tomar el control del vehículo en caso de emergencias ayudas a discapacitados

5 Arquitectura ISAAC Segmento base Vehículo Vehículo Vehículo Base GPS Estación base Conductor Controlador Ayudas Visión escénica Segmento base Sensores Actuadores Equipo embarcado

6 Arquitectura Embarcada Receptor GPS Conductor Sistema inercial Controlador IR - US Volante Monitor conductor Cámara Acelerador Sistema avisador Sistema laser Sistema sensorial Freno Actuadores Actuador universal Sistema de ayuda

7 Relaciones Funcionales Datos GPS Mapa Visión fija Sensores distancia Escena global Monitor tráfico Sensores inerciales Escena local Visión embarcada Actuadores Control vehículo Conductor Guante datos Monitor

8 Imágenes y Vídeos (I)

9 Imágenes y Vídeos (II)

10 Imágenes y Vídeos (III)

11 Imágenes y Vídeos (IV)

12 Imágenes y Vídeos (V)

13 Primeros Resultados en Control Fraccional

14 Introduction Performance comparison of an AGV with a spatial controller (ε-controller) for path tracking using several control schemes: P PI PI α (FOC)

15 The ε-controller (I) Path-tracking algorithm that operates on the vehicle normal deviation (ε) from the path. Generates a desired velocity vector V I* which depends on ε. Relationship between ε and V I* depends on the kind of controller (P, PI, PI α, etc).

16 The ε-controller (II) Cascade control architecture MakeSetPoint (MSP) algorithm converts V I* into body-fixed longitudinal velocity (v w *) and steering angle (δ w *) setpoints. Low-level controllers (C w ) track the actuator-level setpoints.

17 Fractional Order Controllers (I) Approximations of fractional order operators Continuous: Evaluations of function techniques Interpolation of function techniques Curve fitting techniques Discrete: Sistematics recursive distribution of poles and zeros Frecuency domain identification Discrete equivalents of continuous approximations Discrete equivalents of fractional operators

18 Fractional Order Controllers (II) Discrete approximation: Considerations for controller realization Digital realization is not a numerical approximation or evaluation: The step is the sampling period Limited by characterictics of microprocessor-based system: Speed: Each system has its own minimum value for the sampling period must perform all the computations required by the control law between two samples. Memory: More number of paramaters in the approximation, more memory required Discrete equivalents in rational form.

19 Fractional Order Controllers (III) Discrete approximation: Used method Trapezoidal rule + Continued Fraction Expansion (CFE): IIR filters less number of terms than FIR to obtain the same approximation D ± α ( z) = T mα CFE 1 ±α z mα Pp ( z = 1 1 T + z Q ( z 1 q ) )

20 P-Controller: Control Strategies Implementation: Digital P regulator with T S =0.1s PI-Controller: Implementation: Digital Integrator using Tustin s rule with T S =0.1s TS ( z + 1) GPI ( z) = K I 2( z 1) PI α -Controller: u( t) = K P ε( t) u( t) t P I 0 = K ε( t) + K ε( τ) dτ u( t) = K ε( t) + K I ε( t) Implementation: Finite dimensional IIR filter with T S =0.1s P I α

21 Calculo Fraccionario en Control y Robótica: Aplicaciones en Robótica Móvil Simulations (I) Vehicle: Citroën Berlingo with Ackerman steering system: allows the front wheels to travel differents distances and describe their respective arcs when cornering Lateral dynamic model: f z f f f y x z r r f f x z r r f f x r r f f x x r f y I l c m c v v I l c l c v I l c l c mv l c l c v mv c c v δ + φ + + = φ & && &

22 Test: Simulations (II) Describe a semicircular path with a radius of 25 m At the maximum speed of 10 m/s (36 Km/h) Comparison parameters: Integral Squared Error (ISE) ISE Overshoot (Ov): maximum deviation from desired path Settling time (t set ): time to reach and keep inside ε 0.01 First zero-crossing time (t zc ): first time to reach ε = 0 = N i= 1 ε 2 i

23 Simulations (III) Simulations Results: Optimum values K P K I α P PI PI α

24 Simulations (IV) Simulations Results: Comparison parameters ISE Ov t set t zc P PI PI α

25 ε vs time Simulations (V)

26 Conclusions and Future Work Conclusions: We have compared several controllers to show their performances in path-tracking problems. A novel and simple regulation scheme, fractional PI α controller, was simulated with good results. Future Work: We will look for sintonization methods for the fractional controllers with the aim of improving their performances.