The robot localization problem is a fundamental and well studied problem in robotics research. Algorithms used to estimate pose on the map are usually based on Kalman or particle ¯lters. These algorithms are able to cope with errors, that arise due to inaccuracy of robot sensors and e®ectors. The performance of the localization algorithm depends heavily on their quality. This work shows performance of localization algorithm based on particle ¯lter with small miniature low-cost E-puck robot. Information from VGA camera and eight infrared sensors are used to correct estimation of the robot's pose.
Parameters Value Maximum translational velocity 12.8 cm / sec Maximum rotational velocity 4.86 rad / sec Stepper motor maximum speed +- 1000 steps / sec Distance between tires 5.3 cm
3 Dead reckoning cumulation. At each step (each time you take an
encoder measurement), the position update will involve
Dead reckoning ([
E-puck is equipped with a di®erential drive (Fig- account. ure 3) - a simplest method to control robot. For a differential drive robot the position of the robot can be estimated by looking at the di®erence in the encoder 4 Image processing values ¢sR and ¢sL. By estimating the position of the robot, we mean the computation of tuple x; y; £ as The robot has a low-cost VGA camera with resolution a function of previous position (xOLD; yOLD; £OLD) of 480x640 pixels. Unfortunately, the Bluetooth conand encoder values (¢sR and ¢sL). nection supports only a transmission of 2028 colored pixel. For this reason a resolution of 52x39 pixels max0 x 1 0 xOLD 1 0 ¢x 1 imizes the Bluetooth connection and keeps a 4:3 ratio. @ y A = @ yOLD A + @ ¢y A (1) This is the resolution we have used in our experiments µ µOLD ¢µ (see Figure 4). Another drawback of the camera is that it is very sensitive to the light conditions. ¢µ = (2) Despite these limitations, camera can be used to detect objects or landmarks. However, the information ¢s = (3) about distance to the landmark extracted from the ¢sR ¡ ¢sL
L ¢sR + ¢sL 2
Localization with a low-cost robot
Fig. 5. The physical parameters of the real camera
(picture taken from [
Landmarks are objects of rectangular shape of size 5x5 cm and three di®erent colors - red, green and blue.
We implemented image processing subsystem, that detects relative position of the landmark from the robot.
Following steps are included:
{ Gaussian ¯lter is used to reduce camera noise ([
color. ([
of the objects on the image. ([
5
As shown previously (Figure 4), pose estimation based
on dead reckoning is possible for short distances only.
For longer trajectories, more clever methods are
needed. These methods are based either on Kalman
¯lter [
The PF possesses three basic steps - state prediction, observation integration and resampling. It works with quantity p(xt) - the probability, that robots is located at the position xt in time t. In the case of PF, the probability distribution is represented by the set of particles. Such a representation is approximate, but can represent much broader space of distributions that, for example, Gaussians, as it is nonparametric.
Each particle x[tm] is a hypothesis, where the robot can be at time t. We have used M particles in our experiment. The input of the algorithm is the set of particles Xt, most recent control command ut and the most recent sensor measurements zt.
The ¯rst step is the computation of temporary particle set X from Xt. It is created by applying odometry model p(xtjut; xt¡1) to each particle x[tm] from Xt. 2. Correction step - Observation integration The next step is the computation of importance factor wt[m]. It is the probability of the measurement zt under particle x[tm], given by w[m] = t p(ztjx[tm]).
Two types of measurements were considered: { Measurement coming from distance sensors Distance sensor (one averaged value for front, left, right and back direction) were used as bumpers only. In case of any contradiction between real state and hypothesis, importance factor was decreased correspondingly. { Measurement obtained from image processing 7
Localization and pose estimation is an opening gate towards more sophisticated robotics experiments. As we have shown, the localization process can be carried out even with low-cost robot. Experiments were executed both in simulation and real environment.
A lot of work remains to be done. The experiments in this work considered static environment only. Addition of another robot will make the problem much more di±cult.
As we have mentioned already, there are certain
areas in the environment, where convergence of the
localization algorithm is very fast - in corners or near
walls. Sensor fusion is the process of combining
senOutput from image processing was compared sory data from disparate sources such that the
resultwith expected position of the landmarks. In ing information is in some sense better than would be
case of any contradiction (colors and relative possible when these sources were used individually. We
angle of landmarks were checked), importance are dealing with sensor fusion of infrared sensors and
factor was decreased. The bigger mismatch, input from camera.
the smaller importance factor was assigned to As a future work, we would like to implement path
the hypothesis. planning, that takes into account performance of the
localization algorithm. Suggested path (generated by
3. Re-sampling path planning algorithm) should be safe (the chance
The last step incorporates so-called importance to get lost should be small) and short. Multi-criterial
sampling. The algorithm draws with replacement path planning will be based on dynamic
programM particles from temporary set X and creates new ming ([