The paper deals with the time optimal control of automatically driven cars modeled with gear shift as discrete control input beside the continuous ones in a test path between corridors. The car is required to avoid a static obstacle or performing double lane change. The problem can be formulated as a mixed-integer optimal control problem (MIOCP). The resulting MIOCP is solved by reformulating it to static mixed-integer nonlinear program (MINLP) using time discretization and direct multiple shooting method. Non-commercial open software packages are applied that substantially use the gradients of the objective function and the Jacobians of the constraints exploiting sparsity. A novel algorithm and implementation is presented for computing the derivatives of the complex state trajectory joining equations. This algorithm was given in the form of matrix differential equations whose structure allowed to compute their solution using RK4 in matrix form. The elaborated method can be applied both for combustion engine and electric driven cars. It can form the basis to generate an offline database of a central general collision avoidance system (CAS) for varying path parameters on a grid which can support real time applications.

The paper deals with the approximately time-optimal control of automatically driven cars modeled with gear shift as discrete control input beside the continuous ones in a path between two path boundaries. The path boundaries are defined by their corner points that may be the result of image processing in real time or prescribed in advance. The path is divided into sections for which separate optimum control problems are solved in a nonlinear moving horizon predictive control (NMHPC) fashion increasing the semi-online character of the approach. In each section the problem can be formulated as a mixed-integer optimal control problem (MIOCP). The resulting MIOCP is solved by reformulating it to static mixed-integer nonlinear program (MINLP) using time discretization and direct multiple shooting method. Non-commercial open software packages are applied that substantially use the gradients of the objective function and the Jacobians of the constraints exploiting sparsity. The elaborated method can be applied both for combustion engine and electric driven cars. It can also form the basis to generate an offline database of a central general collision avoidance system (CAS) for varying path parameters on a grid which can further support real time applications.

The paper deals with the time optimal control of automatically driven electric cars in a test path under state and input constraints. The problem can be formulated as a dynamic nonlinear optimal control problem (DNOCP). The resulting DNOCP is solved by reformulating it to a static nonlinear program (NLP) using time discretization and direct multiple shooting methods. A novel method is presented to convert the optimal solution obtained using the single-track model to the optimal control of four-in-wheels-motors driven (4WD) cars. The conversion assures similar motion of the COG of both models and optimal distribution of the longitudinal wheel forces. A discrete model predictive control (MPC) is proposed for the linearized 4WD vehicle model under perturbations which uses the distributed wheel forces and optimizes the perturbations with analytically solvable end constraints. The elaborated method can form the basis to generate an offline database of a general collision avoidance system (CAS).