% Copyright (C) 1993-2013, by Peter I. Corke % % This file is part of The Robotics Toolbox for MATLAB (RTB). % % RTB is free software: you can redistribute it and/or modify % it under the terms of the GNU Lesser General Public License as published by % the Free Software Foundation, either version 3 of the License, or % (at your option) any later version. % % RTB is distributed in the hope that it will be useful, % but WITHOUT ANY WARRANTY; without even the implied warranty of % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the % GNU Lesser General Public License for more details. % % You should have received a copy of the GNU Leser General Public License % along with RTB. If not, see . % % http://www.petercorke.com %%begin % Our localization system requires a number of components: % * a vehicle % * a map that defines the positions of some known landmarks in the world % * a sensor, a range-bearing sensor in this case % * a localization filter, specifically the Monte-Carlo style "particle filter" % Creating the vehicle. First we define the covariance of the vehicles's odometry % which reports distance travelled and change in heading angle V = diag([0.1, 1*pi/180].^2); % then use this to create an instance of a Vehicle class veh = Vehicle(V); % and then add a "driver" to move it between random waypoints in a square % region with dimensions from -10 to +10 veh.add_driver( RandomPath(10) ); % Creating the map. The map covers a square region with dimensions from % -10 to +10 and contains 20 randomly placed landmarks map = Map(20, 10); % Creating the sensor. We firstly define the covariance of the sensor measurements % which report distance and bearing angle W = diag([0.1, 1*pi/180].^2); % and then use this to create an instance of the Sensor class. sensor = RangeBearingSensor(veh, map, W, 'animate'); % Note that the sensor is mounted on the moving robot and observes the features % in the world so it is connected to the already created Vehicle and Map objects. % Create the filter. The particle filter requires a likelihood function that maps % the error between expected and actual sensor observation to a weight. The Toolbox % uses a 2D Gaussian for this and we need to describe it by a covariance matrix L = diag([0.1 0.1]); % The filter also needs a noise model to "drift" the particles at each step, that % is the hypotheses are randomly moved to model the effect of uncertainty in the % vehicle's pose Q = diag([0.1, 0.1, 1*pi/180]).^2; % the values of this matrix should be consistent with the vehicle uncertainty % model V given above. % Now we create an instance of the particle filter class pf = ParticleFilter(veh, sensor, Q, L, 1000); % and connect it to the vehicle and the sensor and give estimates of the vehicle % and sensor covariance (we never know this is practice). The last argument % is the number of particles that will be used. Each particle represents a hypothesis % about the vehicle's pose and a weight (or likeliness). % Now we will run the filter for 200 time steps. At each step the vehicle % moves, reports its odometry and the sensor measurements and the filter updates % its estimate of the vehicle's pose. % % The green dots represent the particles. We see that initially the pose % hypotheses are very spread out, but soon start to cluster around the actual pose % of the robot. The pose is 3D (x,y, theta) so if you rotate the graph while the % simulation is running you can see the theta dimension as well. pf.run(200); % all the results of the simulation are stored within the ParticleFilter object % First let's plot the map clf; map.plot() % and then overlay the path actually taken by the vehicle veh.plot_xy('b'); % and then overlay the path estimated by the filter pf.plot_xy('r'); % which we see are pretty close once the filter gets going, the initial estimates % (when the particles are spread widely) are not so good. % The uncertainty of the estimate is related to the spread of the particles and % we can plot that plot(pf.std); xlabel('time step'); ylabel('standard deviation'); legend('x', 'y', '\theta'); grid