Safe and Efficient Optimization-Based Trajectory Planning in Dynamic Environments Using Conformal Prediction

Due to safety requirements, trajectory planning algorithms that are able to handle uncertain surroundings are becoming increasingly attractive in the field of advanced navigation systems. In this thesis, numerical optimal control techniques are integrated with Conformal Prediction (CP) methodologies, resulting in an efficient class of optimization-based trajectory planning algorithms to meet the aforementioned demands, specifically in the case of non-interacting environments. The main focus is on the formulation of collision avoidance constraints between agents and dynamic obstacles of uncertain pose, both represented as convex sets. 
State-of-the-art algorithms in this field apply the Hyperplane Separation Theorem (HST) to establish sufficiently smooth separating constraints between convex sets of certain pose. Apart from their compatibility with off-the-shelf numerical optimization solvers, these algorithms provide geometry-based initialization techniques for all auxiliary optimization variables, in order to increase overall computational performance and the quality of the optimal solution. 
In addition, CP tools have recently been utilized to capture the uncertainty in the state of dynamic obstacles. Approximate prediction regions of high confidence for the obstacles’ trajectories can be constructed and thereafter integrated into Model Predictive Control (MPC) strategies, providing probabilistic collision avoidance and recursive feasibility guarantees. The latter are achieved by formulating non-smooth, gradually relaxed collision avoidance constraints.  
In this work, elements of convex geometry including the HST are combined with CP tools to construct sufficiently smooth collision avoidance constraints for efficient, optimization-based trajectory planning in uncertain environments. The collision avoidance and the recursive feasibility guarantees as well as the efficiency of the proposed algorithms is tested in the context of autonomous parking of tractor vehicles.
 

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