Symbolic dynamics and model-based control of autonomous vehicles

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Autonomous driving technologies will transform the automotive sector, greatly increasing vehicle safety and transportation efficiency, and providing low-cost mobility to thousands unable to handle the task of driving on their own. Private and public sector investment is ramping up in the expectation of significant progress over the next few years. Google's ambitious program promises fully automated vehicles by 2020, but Google's very expensive state-of-the-art vehicles are achieving only 2000 km between forced disengagements of the driverless system.**A promising technology to control autonomous vehicles so that they avoid static objects and moving cars or pedestrians is known as "model-predictive control". Essentially, a dynamic model of the car predicts a short time into the future; the controller uses this prediction to control the steering, brakes, and throttle. The better the model, the better the control. However, the model-predictive controller must run very quickly on a car's computers, especially when emergency maneuvers are required.**Symbolic computing is a technology pioneered and commercialized by Maplesoft. It allows the direct manipulation of the mathematical equations within the model and controller. Not only can the equations can be simplified symbolically, they can be used to generate extremely fast simulation code - such as that needed by an autonomous vehicle.**The goal of this research is to develop new theories and symbolic computing software that automatically generates very fast model-predictive controllers; the target application is the University of Waterloo's AutonoMoose, the first autonomous vehicle approved for Ontario's roads. The proposed new theories and Maplesoft-based algorithms will improve the performance of vehicle controllers, and accelerate the development of autonomous vehicles in Canada and abroad. In turn, this will increase the adoption of Maplesoft software by automotive manufacturers and researchers around the world.****