Unconstrained Quadratic Programming Problem with Uncertain Parameters

In this paper, an unconstrained quadratic programming problem with uncertain parameters is discussed. For this purpose, the basic idea of optimizing the unconstrained quadratic programming problem is introduced. The solution method of solving linear equations could be applied to obtain the optimal solution for this kind of problem. Later, the theoretical work on the optimization of the unconstrained quadratic programming problem is presented. By this, the model parameters, which are unknown values, are considered. In this uncertain situation, it is assumed that these parameters are normally distributed; then, the simulation on these uncertain parameters are performed, so the quadratic programming problem without constraints could be solved iteratively by using the gradient-based optimization approach. For illustration, an example of this problem is studied. The computation procedure is expressed, and the result obtained shows the optimal solution in the uncertain environment. In conclusion, the unconstrained quadratic programming problem, which has uncertain parameters, could be solved successfully.

Efficient and Safe Motion Planning for Quadrotors Based on Unconstrained Quadratic Programming

SUMMARY An autonomous motion planning framework is proposed, consisting of path planning and trajectory generation. Primarily, a spacious preferred probabilistic roadmap algorithm is utilized to search a safe and short path, considering kinematics and threats from obstacles. Subsequently, a minimum-snap and position-clearance polynomial trajectory problem is transformed into an unconstrained quadratic programming and solved in a two-step optimization. Finally, comparisons with other methods based on statistical simulations are implemented. The results show that the proposed method achieves computational efficiency and a safe trajectory.