Just keep rolling a lawn ION's autonomous mowers: you might not know it from your own backyard performance, but mowing a lawn accurately and precisely constitutes a difficult systems problem, requiring centimeter-level accuracy and precision control for straight lines and smooth turns. Three student teams answered the Institute of Navigation's call to produce a smarter-than-the-average lawnmower

GPS World, Sept, 2004 by Mikel Miller, John Raquet, Jade Morton, Frank Van Graas, Boris Pervan, Laura O'Rear

Leonard, an automated ground vehicle (AGV), performs trajectory-tracking operations. Carrier-phase differential GPS (CDGPS) measurements are fed back to the controller, which sends optimal correction commands to the motors.

IIT opted for a differential-drive vehicle concept for its simplicity and robustness. Steering is performed by differencing angular velocity measurements from two opposing driving wheels. The actuators consist of two DC motors with gear-and-belt type reducers. The power is delivered by two 12V DC batteries that provide up to four hours of autonomous operation. All components except the antennae and wheels are enclosed in a waterproof and dustproof rugged aluminum frame. Two floating casters ensure vehicle balance and stability.

The lawnmower is a separate module rigidly mounted on the mobile platform. It carries its own 12V DC battery that powers a motor directly linked to a 15-inch cutting blade. The mower can operate for up to 45 minutes.

Sensors and Computer. The DGPS sensor is composed of a GPS receiver and a spread spectrum data link in communication with the reference station. The GPS patch antenna is fixed at the center of an aluminum plate to minimize the effects of multipath reflections. Also, low cost optical encoders are integrated to the motor driving shafts.

An embedded computer equipped with a data acquisition card processes the sensor data and sends commands to the motors via speed-controller interfaces. The speed controllers, or motor drives, provide the necessary amperage to the motors at the computer's request. A wireless system enables remote control, and can provide real-time monitoring.

Control System. The navigation and guidance control system is based on a detailed dynamic model. Linearized along the desired trajectory, at a constant velocity of 2 kilometers/hour, the equations of motion for the vehicle result in a fifth-order state space representation.

The control system, a discrete closed-loop feedback algorithm, uses a linear quadratic regulator (LQR) whose controller performance index weights are distributed to minimize cross-track error and avoid drive-motor saturation regions.

A seventh-order Kalman filter using CDPGS sensor inputs provides the basis for state estimation. Optimal performance of the estimator requires that process and sensor noise be accurately modeled. The team derived and implemented detailed random process models in terms of vehicle design parameters to account for disturbances such as ground slope and rugged terrain. The correlation of the GPS measurements due to multipath reflections is modeled with a first-order Markov process.

The controller's time constant (here 0.5 seconds) is limited by both the actuator's bandwidth and the DGPS update rate, and determines the frequency per unit distance of the cross-track-error corrections, for a given vehicle velocity.

The control strategy for mowing a rectangular field takes advantage of the forward/backward motion capability of the vehicle. It aims to simply to go back and forth straight along the field, each trip offset by the width of the cutting blade. More elaborate tactics are considered for future work. In particular, Leonard has the capability to operate at various speeds (that could change depending on the proximity of the mower to the field's edges), and can perform zero-radius turns.