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This paper examines a symbolic numerical approach to optimize a vehicles track for autonomous driving and collision avoidance. The new approach uses the classical cost function definition incorporating the essential aspects of the dynamic state of the vehicle as position, orientation, time sampling, and constraints on slip angles of tires. The optimization processes minimize the cost function and simultaneously determine the optimal track by varying steering and breaking amplitudes. The current velocity of the vehicle is limited to a maximal velocity, thus, allowing a stable search of the optimal track. The parametric definition of obstacles generates a flexible environment for low and high speed simulations. The minimal number of influential optimization variables guarantees a stable and direct generation of optimal results. By the current new approach to control a vehicle on an optimal track, we are able to autonomously move the vehicle on an arbitrary track approximated by low order polynomials. The optimization approach is also able to deal with a variety of different obstacles and the corresponding optimal smooth obstacle path. The computations demonstrate the effective control of a four wheel vehicle in normal operation and exceptional obstacle avoidance with continuously differentiable obstacle avoidance tracks. Simulation tests are done using vehicles velocities of 3, 6, 7.6, 10, 12, and 18&#x00A0;m/s. At higher vehicles velocities, a mathematical-only approach is not sufficient and a mechanical intervention for tires is needed as a complimentary part to control the slip angle. The results shows that the cost function reached a considerably high average convergence-to-zero rate success in most of the tested scenarios.

Vehicle Risk Assessment and Control for Lane-Keeping and Collision Avoidance at Low-Speed and High-Speed Scenarios