Measuring Cooperative Robotic Systems Using Simulation-Based Virtual Environment Xiaolin Hu Computer Science Department Georgia State University, Atlanta GA, USA Bernard P. Zeigler Arizona Center for Integrative Modeling and Simulation University of Arizona, Tucson AZ, USA 85721

Agenda Background on DEVS and Model Continuity The Virtual Measuring Environment The Robotic Convoy Example Preliminary Simulation Results Future Work

Derived from mathematical dynamical system theory Based on a formal M&S framework Supports hierarchical model construction  Atomic model  Coupled model Explicit time modeling DEVS (Discrete Event System Specification) real

DEVS Formalism

A Background on Model Continuity for Robotic Software Development The control logic to be designed Real environment Sensor/actuator Robotic system to be Designed Control model Environment model Virtual Sensor/actuator Simulation & Test Modeling Control model Real environment Sensor/actuator interface System in Execution Mapping

A Virtual Measuring Environment A virtual measuring environment – an intermediate step that allows models and real robots to work together within a “virtual environment” Simulation-based measuring using robot models and the environment model Real system measuring with all real robots within a real physical environment This virtual measuring environment will bring simulation- based study one step closer to the reality.

Realization of the Virtual Measuring Environment Model Continuity allows the same control models used in simulation to be deployed to real robots for execution. The couplings among these models are maintained from simulation to execution. The clear separation between the control model and sensor/actuator interface make it possible for the control model to interact with different types of sensors/actuators, as long as the interface functions between them are maintained. The control model of a real robot can use real sensors/actuators to interact with the real environment and virtual sensor/actuators to interact with a virtual environment. A real robot can communicate with robot models simulated on computers, resulting in a system with combined real and virtual robots.

virtual environment virtual obstacle virtual robots computer virtual counterpart of the real robot Control Model virtual sensorsHIL actuators wireless communication mobile robot Architecture of the Virtual Measuring Environment

An Incremental Measuring Process Robot Model Robot Model Virtual Environment Virtual Sensor Virtual Actuator Virtual Sensor Virtual Actuator (a) Conventional simulation Robot Model Real Robot Virtual Environment Virtual Sensor Virtual Actuator Virtual Sensor HIL Actuator (b) Robot-in-the-loop simulation Real Robot Real Robot Real Environment Real Sensor Real Actuator Real Sensor Real Actuator (c) Real system measurement

Experimental Frames input stimuli: specification of the class of admissible input time-dependent stimuli. This is the class from which individual samples will be drawn and injected into the model or system under test for particular experiments. control: specification of the conditions under which the model or system will be initialized, continued under examination, and terminated. metrics: specification of the data summarization functions and the measures to be employed to provide quantitative or qualitative measures of the input/output behavior of the model. Examples of such metrics are performance indices, goodness-of-fit criteria, and error accuracy bound. analysis: specification of means by which the results of data collection in the frame will be analyzed to arrive at final conclusions. The data collected in a frame consists of pairs of input/output time functions.

An Architecture with Experimental Frames Robot Models Environment Model Experimental Frames Define input stimuli, control, metrics, analysis from the measuring point of view Model how the environment reacts/interacts with robots Control model of robots Models of sensors and actuators

Robot2 BReadyIn FReadyIn FReadyOut BReadyOut Robot3 BReadyIn FReadyIn FReadyOut BReadyOut FReadyOut Robotn FReadyIn Robot1 BReadyIn BReadyOut… A Robot Convoy Example Robots are in a line formation with each robot has a front neighbor and a back neighbor. The system try to maintain the coherence of the line formation A robot’s movements are synchronized with its neighbors A robot (except the leader robot) goes through a basic “turn – move – adjust – inform” routine. No global communication/coordination exists.

Avoid Convoy HWInterface activity move FReadyOutFReadyIn moveComplete move BReadyInBReadyOut FReadyOut BReadyOut FReadyIn BReadyIn Based on Brooks’ Subsumption Architecture The Avoid model controls a robot to move away if the robot collides with anything. The Convoy model is fully responsible to control a robot to convoy in the team. HWInterface activity is responsible for the sensor/actuator hardware interfaces. Robot Model

ii  i-1 ii  i-1 a d i-1 didi D RiRi R i-1 ii RiRi Formula of Movement

move1 sensorData1 sensorDataN startMove TimeManager1 Robot1 t1 SpaceManager Robot1 (x, y) RobotN (x, y) Obstacles (x, y) moveComplete1 moveNstartMove TimeManagerN RobotN tN moveCompleteN …… …… … This TimeManager determines how long it takes for a robot to finish a movement. The SpaceManager is a model of the experimental floor space, including the size, shape and position of the work area, the static objects and robots. In this example we have ignored the detailed dynamic processes of a movement. Environment Model

Two Noise Factors Random numbers are used to simulate the noises and variances in robots’ movement. d a D Distance noise factor (DNF): the ratio of the maximum distance variance as compared to the robot’s moving distance. Angle noise factor (ANF): the ratio of the maximum angle variance as compared to the robot’s moving distance.

Formation Coherence The formation coherence is affected by the noise factors. We use the average position error of the robot team as the indicator for the convoy system’s formation coherence: the smaller the error is, the more coherent the convoy system is. The position error does not accumulate over time – coherent.

Series 1: DNF = 0.04, ANF = 0.04, average = Series 2: DNF = 0.1, ANF = 0.08, average = Series 3: DNF = 0.2, ANF = 0.1, average = Noise Sensitivity The system is insensitive to the noise factors as long as these factors are within a safe boundary.

Scalability It shows that the average position error increases as the number of robot increases. If this trend holds true with more robots, the system is not scalable in the sense that it will eventually break as more robots are added into the system.

Robot_1Robot_kRobot_n …… Environment Model Real environment abstract sensors – abstract motor abstract sensors – HIL motor real sensors – HIL motor A Future Experimental Setup For example, we can check the back robot’s position errors based on the position and direction of its front robot in the physical environment.

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