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Summary
Summary
Dead-reckoning via encoders on wheeled-mobile robots is a simple but inaccurate method to estimate position. The major drawback of encoders is wheel slippage errors that accumulate over time. This problem is often addressed by using additional sensors such as compass, gyroscope, or GPS. This paper details the integration and effectiveness of a relatively low-cost solution using an electronic compass to reduce positioning error on a wheeled tricycle mobile robot (Figure 1). A customised Visual Studio program has been developed to adjust the settings of the electronic compass and integrate it with the Visual Studio based robot control system. The electronic compass heading data is fused with the encoder odometry heading data in three different ways: simple fusion, linear weighted fusion, and Kalman filter fusion. Simple fusion and linear weighted fusion rely on parameters determined from angular acceleration and angular velocity, respectively. The Kalman filter uses variance data for the encoders and electronic compass to determine an optimal heading. Experiments have been conducted in an indoor corridor environment to evaluate and compare the various fusion methods. Position error is successfully reduced and is sufficient to locate the robot within the corridor.
The threshold value for simple fusion has been selected based on the dynamic characteristics of the robot. Multiple tests of the robot in straight and circular paths within the dimensions of the corridor were used to estimate typical values of angular acceleration. Based on the collected data, the threshold for simple fusion is empirically set to 0.37 rad/s2.
Three types of encoder heading weighting functions have been selected for linear weighted fusion. These weighting functions are: linear, non-linear piecewise, and fuzzy rule-based . Each of the three encoder weighting functions is illustrated in Figure 2. The main purpose of the functions is to give preference to the compass heading when the robot has low angular velocity. Weights and threshold values for each function have been empirically selected based on manual operation of the robot in the corridor and labs.
Kalman filter fusion requires values for process variance Q and measurement variance R. The encoder provides good accuracy over short distances (<= 5 m). From straight line tests with a maximum speed of 0.3 m/s to reduce wheel slippage, the standard deviation was determined to be approximately 1.5º. Thus, the process variance Q is approximately 2.25º. On the other hand, the compass provides reliable readings over long distances. Its standard deviation is approximately 3º. Hence, the measurement variance R is approximately 9º.
Figure 3 shows position estimation using the encoders only. For comparison, Figure 4 shows the results achieved with the Kalman filter. For an overall comparison, the estimated positions produced by each fusion method have been plotted on a single graph and magnified to view the similarity at various sections of the corridor. Figure 5 highlights the estimated position in the upper section of the corridor. Figure 6 and 7 illustrate the estimated positions towards the end of path. All three figures show the red and magenta lines corresponding to simple fusion and Kalman filter fusion tracking closest to the waypoints. Table 1 details the maximum error, mean error, and standard deviation from all waypoints. The lowest errors have been achieved for simple fusion and the Kalman filter.
Figure 1. Electronic compass module and placement on mobile robot.
Figure 2. Encoder weighting functions for linear weighted fusion.
Figure 3. Position estimation with only the encoders.
Figure 4. Position estimation improvement with Kalman filter.
Figure 5. Comparison in upper section of corridor.
Figure 6. Comparison at second last waypoint.
Figure 7. Comparison at last waypoint.
Table 1. Error analysis from all waypoints.
For more details on this project refer to the following:
Journal Paper:
Chand, P. Integrating an Electronic Compass for Position Tracking on a Wheeled Tricycle Mobile Robot, Drone Systems and Applications (formerly Journal of Unmanned Vehicle Systems). (accepted) (https://cdnsciencepub.com/doi/abs/10.1139/dsa-2021-0049)
Full text available at: https://cdnsciencepub.com/doi/pdf/10.1139/dsa-2021-0049
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