Mobile robots SOFA-2009 and “Phoenix-3” Alex Astapkovitch, head of the Student Design Centre State University of Aerospace Instrumentation Alex Burdukov, student, “Phoenix-3” project leader SOFA-2009 Virtual robot benchmark model Real robots: Virtual robots: “Phoenix-3” -Phoenix Robotics Group-

Virtual robot SOFA Mobile robots are complex electromechanical devices the real experiments are very expensive in sense of time and stuff. - During Phoenix-2 project a virtual environment and simplified robot model were developed to generate on board cameras images. - Phoenix-3 project is the third step of Phoenix student research group that consists from the hardware development and the background theory activities. - The strategic goal of the “Phoenix-X” projects is a developing of understanding of the learning strategy for the control system on base of a neuron net. - SOFA-2009 was started as scientific support for “Phoenix-3” project and still is the part of “Phoenix-X” student research activity, but now... It is a free ticket on fast train for young researches to Computational Robotics field valley !

Virtual robot SOFA Main goal of SOFA is introduction to robotic society the benchmark model than can be used to investigate neuron net control system learning. Research activities of Phoenix research group is concerned of “Teaching by Showing” approach for multi channel real time control systems, based on artificial neural net. -The model has to be as simple as possible and of autonomous differential drive wheel robot is used as legend. SOFA-2009 benchmark model formulated as system of ordinary differentional equations: dx/tx =f(x)+U(t) X(0)=X0 -MathCAD 14 was used as a tool due to friendly and fast user interface.

Virtual robot SOFA-2009 Kinematics and dynamics models of virtual robot SOFA axe x direction “forward” φ(t) – robot angle position axe y axe x earth fixed frame R с (t)– robot center position vector R 0 (t) - instant center of arc R(t) – instant rotation radius φ (t+∆t)- φ (t) = ∆ φ (for left wheel) = ∆ φ (for right wheel) R 0 (t) = R 0 (t+∆t) Basic relations:

Virtual robot SOFA-2009 Model SOFA-2009 is defined with parameters set : Dw = 0.3 Lr = 0.5 Jr = 0.25 k11 = k22 = 75 k12 = k21 = 10 Rm = 0.1 Lm = 0.01 k13 = k23 = 1.5 Vmax = 12 Vmax is the maximal absolute value for accumulator voltage. Model includes dynamic equations, gear model for every wheel, motor model, control system model. The simplest as possible model consists of 7 ODE with at least 9 parameters.

Control voltages: U 1 (t) =0 U 2 (t) = U max = 12 V. Control voltages: U 1 (t) = U 2 (t) = U max = 12 V. Virtual robot SOFA-2009 TEST_1. Moving forward with speed 4/5 m/sec TEST_2. Rotation around left wheel with ang. speed π /4 r/s SOFA-2009 model testing Rc(0) X,Y = 0 φ(0) = 0

Virtual robot SOFA-2009 Transfer function Vout Vin Actor layer neuron Vmax, Vmin Uout Left Motor Uout Right Motor AFSS APS ASS Sensor layer Left motor control channel W left = [w 0l,w 1l,w 2l ] Right motor control channel W right = [w 0r,w 1r,w 2r ] Uin left Uin right APS – Angle Position Sensor ASS – Angle Speed Sensor AFSS – Angle Final Speed Sensor Example of neuron control system:

Virtual robot SOFA-2009 S 1 (T 1 ) S 2 (T 1 ).. S n (T 1 ) S 1 (T 2 ) S 2 (T 2 ).. S n (T 2 ) …………………… S 1 (T p ) S 2 (T p ).. S n (T p ) w1w2wnw1w2wn A 1 (T 1 ) A 1 (T 2 ) A 1 (T p ) * = S * w = Ua Matrix form One step learning paradigm idea: minF(w) = (Sw - Ua, Sw – Ua) +  (w,w) w Tixonov regularization w = (S T S +  E) –1 S T Ua Weights calculation

Virtual robot SOFA-2009 Experiment with virtual robot includes at least three steps:  sample generating and neuron net control system learning ;  simulation of the robot dynamics with "learned "neuron net control system;  research experiments. 1. SAMPLE GENERATING AND NEURON NET LEARNING Final position vector X(T1), velocity vector V(T1) SOLUTION TABLE [t i, X (t i ) ] Sensor System Model Weight Matrix Calculation W= (S t S +γE) -1 S t Ua NEURON NET CONTROL SYSTEM STRUCTURE Cauchy problem solution for [T0 -T1] Control voltage matrix (vector Ua(t) for every motor ), that corresponds to robot mission Initial position vector X0 Robot model

Virtual robot SOFA-2009 Initial and final positions, control net structure depends on research PROBLEM NEURON NET CONTROL SYSTEM MODEL Cauchy Problem Solution POST PROCCESINGS NEURON NET CONTROL SYSTEM MODEL Cauchy problem solution and estimation Initial position Final position Robot model 2. CONTROL SIMULATION 3. NUMERICAL EXPERIMENTS Examples are presented in applications to articles and in site

Virtual robot SOFA-2009 Example of the supervised learning for π/4 rotate to left sample: Sample rotation to left with maximal velocity learning sample of control voltages for left and right motors preliminary estimation of the trainingestimation of the robot dynamics under neuron net control system for π/4 rotate to left for limited and unlimited actor voltage

Virtual robot SOFA-2009 rotation to left on π with limited and unlimited Vmax motor currents for limited and unlimited voltage phase portrait for unlimited case: start point (0,0),final (3.14,0) phase portrait for limited Vmax: start point (0,0),final (3.14,0) Sample of autonomous operation for π rotate task:

Virtual robot SOFA MathCAD 14 example code presented in article as appendix to articles A. Astapcovitch “Virtual mobile robot SOFA-2009 for Computational Robotics Research”; A. Burdikov “Autonomous Robot “PHOENIX-3”” SOFA 2009_TEST1_2.xmcd- SOFA model test SOFA 2009_A_LEARNING.xmcd- learning to rotate SOFA 2009_DISTANCE_LEARNING.xmcd- learning to move ahead SOFA 2009_AD_LEARNING.xmcd- learning to reach the prescribed 2D point - Virtual robot SOFA-2009 with neural net control system and learning procedure can be downloaded for free from the site - Site section SOFA-2009 has examples:

Autonomous Robot “PHOENIX-3” Autonomic robot Phoenix-3 is designing to be able to patrol the determined area with the purpose of detection the centers of the flame. In case of the flame detection the robot should come nearer and use the onboard fire extinguisher to eliminate flaming. For orientation the video shock-proof camera with the rotary mechanism and a zoom lens is supposed to be used. Project legend:

Autonomous Robot “PHOENIX-3” -There are several steps in neural system synthesis using “teaching by showing” methodology. - During the 1st step robot’s movement are controlled by a traditional control system or by operator. During this procedure robot’s sensors information and control commands are written to onboard laptop. -This data is used on the 2nd step for neural regulator coefficients determination. - It means that the control system has to have at least two basic modes of operations: operator control mode and autonomous operation. - Operator control mode is used during the learning phase.

Autonomous Robot “PHOENIX-3” Control system structure during autonomous operation: Controller ASK-Lab Left and Right Motor Control Bridges Rotating camera (sensor) Multichan nel Video IP-codec ASK-Lab Laptop Fire extinguisher engine Actors Sensors RS-232 Rotating camera (position motors) RS-485 Ethernet Ultrasonic Orientation System CANbus Still Camera

Autonomous Robot “PHOENIX-3” Wi-Fi AP Computer Video link RF-transmitter cam. output 1 cam. output 2 Pad 1 (robot) Pad 2 ( fire extinguisher ) Operator Radio link Control system structure for operator control mode: -During Phoenix-2 experiments, two control schemes were tested – one with analog and one with digital control channel. -It was noticed, that digital control system has significant delays in the channel, so it was decided to use an analog control system for Phoenix-3 project.

Autonomous Robot “PHOENIX-3” Analog joysticks RF-transmitterRF-receiverController Laptop Actors and sensors Two channel RF-control system. -Phoenix-3 project implements two channel control system: one for robot movement control and another for control on board equipment. -Hitec FOCUS 6 RC-equipment was used during experiments. It includes a control pad and receiver module.

Autonomous Robot “PHOENIX-3” Ultrasonic Orientation System. 1 – MCP 2510 CANbus controller chip; 2 – PIC18F458 microcontroller chip; 3 – 16-bit counter; 4 – ultrasonic pulses generator; 5 – ultrasonic receiver; 6 – ultrasonic transmitter; 7 – frequency divider; 8 – quartz generator. - Ultrasonic distance measuring module based on MuRata MA40S8S and MA40S8R devices was developed. Has a net structure based on CANbus. - Developed module can measure of distances up to to 2 m. with accuracy resolution approx. 0,2 mm CANbus module structure: 5 6

Autonomous Robot “PHOENIX-3” It was demonstrated during Phoenix-1 project that camera inclination sensor is the necessary element of control system. Video subsystem. “Phoenix-3” video subsystem of the robot includes a rotary shock-proof camera with the rotary mechanism, a zoom lens and a two-channel video digitizing module with an Ethernet interface. SEN= S1 S2 SN This column is filed by “hand ” with camera inclination angle value specific for every learning sample SI. Algorithm of using fixed inclination angle:

Autonomous Robot “PHOENIX-3” -More info about project “Phoenix-3” can be find on the site