The robotic vehicles testbed at the UCLA Applied Mathematics Laboratory consists of several components that cooperatively allow for experimental evaluation of dynamical systems and control theories. The following components play an essential role to the testbed: the robotic vehicles, the vision system and the experimental observation bed.

The robotic vehicles consist of an RC toy car base taken from the ZipZaps line of toys. This base contains two motors, one allowing for variable steering and the other for speed control. The RISC processor, an Atmel Atmega8, allows for onboard decision making and data collection through several ADC channels. The processor controls the speed and steering via pulse-width modulation. An onboard communications unit, the Radiotronix Wi.232DTS, maintains a wireless connection with the vision system as well as an optional data-logging computer. The robotic vehicles also possess a unique ID tag that allows for easy identification for the vision system.

The vision system consists of two cameras looking directly down onto the experimental observation bed. The cameras are connected via IEEE1394 to a standalone computer running software written with OpenCV in C++. The developed software tracks the robot's identification tag and wirelessly relays location information to the vehicle. The vehicle may then make decisions based on its current or previous location.

The observation bed is a rectangular piece of carpet. The cameras observe a 640x890 pixel portion of the bed, where 1 pixel is approximately 0.0937 inches.

For more information on the second generation testbed, please see [1].

Due to a robot's ability to explore areas which forbid direct human exploration, boundary tracking is a very important field of dynamic control.

One algorithm proposed for the tracking of boundaries by autonomous vehicles is the UUV-gas algorithm [2]. The algorithm,

varies the orientation of the vehicle &theta_next by taking the previous vehicle orientation &theta_prev and adding a constant to it that depends on the state of the vehicle with respect to the boundary.

Another proposed algorithm provides control similar to the UUV-gas algorithm but depends on the time between boundary crossings. The algorithm,

is proposed in [3]. The algorithm requires &theta_ref as a reference angle, as well as t^~, which is the time between the current and previous crossing of the boundary.

To eliminate excessive debugging caused by implementing too many new components at once, the algorithm was tested with a software-based virtual boundary. The vehicle possessed a priori knowledge of the boundary it was supposed to track. As a result, the coded algorithm could be debugged while abstracting away the sensor. Figure 1 shows the vehicle tracking a virtual rectangle with the UUV-gas algorithm. It clearly shows that the vehicle's trajectory covers a large amount of space irrelevant to the boundary, thus rendering it inefficient. Further, it also possesses a large risk of becoming unstable, disallowing it the ability to track the boundary at all.

The time-dependent algorithm shows greater promise, as seen in Figure 2. The vehicle, travelling clockwise around the rectangle, starts with a wide initial condition but appears to be qualitatively more efficient than the UUV-gas algorithm. When the speed of the vehicle is increased, however, the algorithm becomes almost as inefficient as the UUV-gas algorithm, as illustrated in Figure 3.

The Fairchild Semiconductor QRB1134 IR sensor was chosen for its low current consumption and ease of being implemented on the vehicle. It consists of an IR phototransistor which acts as an NPN BJT and an IR LED. The phototransistor was wired in an emitter follower configuration and its output was attached to an ADC channel on the Atmega8. Figure 4 shows the final installation of the sensor on the vehicle.

The physical boundary is modeled by a concave curve as shown in Figure 5. Tracking this boundary would no longer require the vehicle to know its current position since all data is acquired a posteriori by the IR sensor, thus rendering the vision cameras obsolete except for data logging. The boundary is created by the junction of the black and teal tapes. Black and teal tapes were used because they provided the greatest difference in voltage readings by the QRB1134. Further, the black and teal tapes were not recognized by the tracking cameras (in the opposite case, tracking data would nealy impossible to obtain for logging purposes).

Due to excessive noise read by the ADC, a method of filtering was required in order to make decisions regarding the vehicle's position with respect to the boundary. Four cumulative sum (CUSUM) filters were used in order for the vehicle to distinguish "outside" and "inside" relative to the boundary.

Lowside CUSUM filters, described by

provide a mean for estimating a falling or negative edge [3]. Here, L(k) represents the CUSUM output, B is the background noise and c_l is a percentage that corresponds to how quickly the filter responds to a change in the raw data reading z(k). The filter is bound by [L_bar, 0].

Highside CUSUM filters, described by

provide a mean for estimating a rising or positive edge [3]. Here, H(k) represents the CUSUM output, B is the background noise and c_u is a percentage that corresponds to how quickly the filter responds ta a change in the raw data reading z(k). The filter is bound by [0,H_bar].

Using two CUSUM filters allowed the following concatenated digital output: 00 while on the gray part of the testbed, 01 while on the black tape and 11 while on the teal tape. Thus, when the microcontroller detected a change in the CUSUM from 01 to 11, it would know that it is currently inside the boundary. When the microcontroller detected a change in the CUSUM from 11 to 01, it would know that it is currently outside the boundary. Figure 6 shows the vehicle's transition from the gray part of the testbed to the black tape to the teal tape and finally to the gray part of the testbed.

As soon as working parameters were identified for the two CUSUM filters, experimental testing was done to determine the efficiency of the UUV-gas algorithm and the time-dependent algorithm. To view the UUV-gas implementation of the vehicle tracking the physical boundary, please see: UUV. To view the time-dependent algorithm implementation, please see: Time-Dependent.

In conclusion, it qualitatively appears that the time-dependent algorithm is more efficient at tracking a physical boundary than the UUV-gas algorithm.