Homework 1 Autonomous Mobile Robots Solution

Description

A document containing the answers and gures should be uploaded to Gradescope as HW1writeup.pdf. All the code and the les needed to run the code are to be uploaded to Canvas as a zip le named HW1code.zip. Speci c functions, as indicated below, should be uploaded to their corresponding assignments on Canvas.

Notes about autograded assignments:

• We highly recommend you develop and debug the autograded functions in Matlab. The error messages that the autograder provides are not as explicit as in Matlab.

• You may submit as many times as you like until the deadline

• Make sure to also include the functions in the zip le you upload to Canvas

Changing Reference Frames (30 Points)

Nearly every robot task requires operating in multiple reference frames. Download and open lidarScan.mat, containing a sample lidar scan (as returned by LidarSensorCreate.m). The 681 data points correspond to the measured ranges (in meters) equally spaced over the angles [ 120 ; 120 ].

1. Edit the le lidar range2xy.m to convert the raw lidar scan into 2D local robot coordinates. Assume the lidar sensor is located at the front of the robot pointing forward (i.e. the sensor pose in local coordinates is [x_l; y_l; _l] = [r; 0; 0], where r is the robot radius). The robot’s x-axis points forward and y-axis points left. Assume the robot radius is 0.2 meters. Submit this function in the autograded assignment Homework 1 lidar range2xy on Canvas.

2. Edit the le robot2global.m to transform any 2D point from the local robot coordinates into global coordinates, given the robot’s pose. Submit this function in the autograded assignment Homework 1 robot2global on Canvas.

3. Edit the le global2robot.m to transform any 2D point from global coordinates into local robot coordinates, given the robot’s pose. Submit this function in the autograded assignment Homework 1 global2robot on Canvas.

4. In the same gure, plot using lidar range2xy.m the lidar scan (points in 2D) in the global reference frame assuming the robot pose is

1. 1. • [3; 4; 2 =3]

1. 1. • [0; 3; =2]

Plot each set of points (corresponding to the scan as viewed by the robot) in a di erent color. Make sure to label your axis and include a legend.

Getting to Know the Simulator and Running a Simple Control Program (20 Points)

Download the MATLAB CreateSim toolbox (download as zip)

https://github.com/autonomousmobilerobots/iRobotCreateSimulatorToolbox

download the latest version of the Matlab Toolbox for the Create from

https://github.coecis.cornell.edu/AMR/MatlabiRobotCreateRaspPi

and add both to your MATLAB path. Review the iRobot Create Simulator User Guide pages 4{10, and the MATLAB Toolbox for the iRobot Create (available on Canvas) pages 11{12.

The le turnInPlace.m is a simple control program that reads the robot’s sensor data and makes the robot turn in place. You can use this function as a template for later functions you will write.

Make sure the CreateSim toolbox is in your MATLAB path and run SimulatorGUI.m. This will open the simulator interface. Click the Load Map button and select box map from the les provided for this homework. Place the simulated robot anywhere on the map by clicking the Set Position button (click once to set the center location, click again to set the heading direction). Run the control program by clicking the Start button in the Autonomous group (bottom right side of the interface) and selecting turnInPlace.m.

1. What does the command SetFwdVelAngVelCreate (line 73 in turnInPlace.m) do? What are the inputs to this function?

2. The left and right wheel velocities are limited to 0:5m/s (observe what happens when you increase cmdV and cmdW on lines 66{67 in turnInPlace.m). Edit the program limitCmds.m to appropriately scale the forward and angular velocity commands so the wheel motors don’t saturate (the shape of the trajectory should be maintained, i.e. do not simply use a max function without making sure the trajectory shape remains the same). Submit this function in the autograded assignment Homework 1 limitCmds on Canvas.

3. Edit turnInPlace.m to use limitCmds.m in the appropriate place, with wheel2Center=0.13 and maxV a value that is less than 0.5. From now on, you should always call limitCmds before sending commands to the robot via SetFwdVelAngVelCreate.m.

4. Write a function backupBump.m to have the robot drive forward at constant velocity until it bumps into something. If a bump sensor is triggered, command the robot to back up 0.25m and turn clockwise 30 , before continuing to drive forward again. Run the simulator and plot the robot trajectory.

Note: To access the sensor data collected during simulation, type global dataStore in the MATLAB Command Window. The ground truth pose of the robot is available in dataStore.truthPose. The sensor data is collected by readStoreSensorData.m; we recommend you take a look at the function to see what sensor information is stored.

5. Write a control function, properly named, to make the robot do something new. What does the function do? Run the simulator using your new control function and plot the robot trajectory.

Feedback Linearization (30 Points)

The iRobot Create is a non-holonomic vehicle, so we can’t send arbitrary V_x and V_y commands to the robot. Instead we must send V and ! commands, as with SetFwdVelAngVelCreate.m. Feedback linearization ap-proximately converts [V_x; V_y] ! [V; !] via a linear transformation.

1. Write a function feedbackLin.m to transform V_x and V_y commands into corresponding V and ! commands using the feedback linearization technique presented in class for a di erential drive robot. (In other words, do not use a turn-then-move control strategy.). Assume the V_x and V_y commands are given with respect to the inertial frame. Submit this function in the autograded assignment Homework 1 feedbackLin on Canvas.

2. In the SimulatorGUI, place the robot near [0; 0] by clicking the Set Position button. For a desired local (body- xed) control input [V_x; V_y]_B = [1; 1], plot the robot trajectory for di erent values of .

3. Write a function visitWaypoints.m to calculate the desired [V; !] controls to drive the robot along a series of waypoints (using feedbackLin.m appropriately). The waypoints are given as a nx2 matrix where each row is the (x,y) coordinate of a waypoint. Keep track of which waypoint is being driven

toward using the index gotopt, and consider the waypoint reached if the robot is within closeEnough of the waypoint location.

4. Using visitWaypoints.m as the control function with = r (the robot radius, 0.2m) and closeEnough= 0:1, plot the robot trajectories for the following sets of waypoints: [-3 0; 0 -3; 3 0; 0 3] and [-1 0; 1 0 ].

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