You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
95 lines
4.1 KiB
95 lines
4.1 KiB
% 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.gnu.org/licenses/>.
|
|
%
|
|
% 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
|