Autonomous Vehicle Control: A Nonconvex Approach for Obstacle Avoidance
This paper develops a two-stage nonlinear nonconvex control approach for autonomous vehicle driving during highway cruise conditions. The goal of the controller is to track the centerline of the roadway while avoiding obstacles. An outer-loop nonlinear model predictive control is adopted for generating the collision-free trajectory with the resultant input based on a simplified vehicle model. The optimization is solved through the generalized minimal residual method augmented with a continuation method. A sufficient condition to overcome limitations associated with continuation methods is introduced. The inner loop is a simple linear feedback controller based on an optimal preview distance. Simulation results illustrate the effectiveness of the approach. These are bolstered by scaledvehicle experimental results.
Most optimization algorithms require convexity to converge to the solution; for this reason, the work in , , and  proposed a convex formulation of the obstacle avoidance problem. The authors achieve convexity by transforming the vehicle-road system from a time-dependent reference frame to a space-dependent one. Obstacle constraints can thus be modeled as a bound on the state, thereby guaranteeing the problem convexity. However, this strategy does not provide a decision as to which side should be used to overtake the obstacle; the preference for passing on the left or right must be established a priori. To overcome this issue, the controller can be divided into a two-stage approach consisting of outer-loop path planning and inner-loop path tracking algorithms. In , an NLMPC is used as a path planner to generate the feasible trajectory. However, the control decision is made using a distance-based method, meaning that the obstacle location cannot be considered a hard constraint. Instead of a constraint, the controller utilizes a repulsive barrier function which, while effective, does not guarantee safety. This paper seeks to add the hard constraint
This paper proposes an outer-loop optimization algorithm based on the generalized minimal residual (GMRES)/ continuation method . This technique is explicit, so the number of mathematical operations to perform at each iteration of the NLMPC is fixed. This ensures a finite computational time for the online solution, as opposed to an unknown computational time for a comparable iterative method, such as in . Moreover, it is based on global optimality conditions, and a nonconvex nonlinear dynamic optimization can be solved. Therefore, obstacles can be considered by the trajectory generation as hard constraints and provide safety guarantees. An important question to be examined is whether the deterministic real-time solution can be performed suitably fast for relevant vehicle implementation.
In this paper, a control architecture is proposed for autonomous vehicle obstacle avoidance during highway cruise conditions. A nonlinear noncovex model predictive control based on a simplified system is used to plan the ideal trajectory and to compute the optimal input. Then, an innerloop linear controller with preview information is used to compensate for the differences between the simple dynamics of the system used in the outer-loop NLMPC and the behavior based on an STVM. The problem is formulated using a curvilinear reference system, and the obstacles are considered in the optimization. Therefore, the problem is reduced to a dynamic nonlinear nonconvex optimization. The algorithm implements a solution based on the global optimality conditions of the minimum principle. Moreover, the proposed control logic is explicit and it guarantees the real-time feasibility. The proposed control logic has been successfully tested on scaled vehicle experimental facilities with encouraging results.
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