Abstract
Sequential convex programming (SCP) has been recently employed in various trajectory planning problems, including entry flight, planetary landing, and aircraft formation. In SCP, convex programming subproblems are sequentially solved to obtain the optimum of original nonconvex problems. For SCP-based quadrotor trajectory planning, this paper proposes a matrix-structure-driven interior point method (MSD-IPM) to improve the efficiency of solving search directions in convex programming. In MSD-IPM, primal-dual systems for solving search directions are derived from the Karush-Kuhn-Tucher (KKT) conditions of quadrotor trajectory planning subproblems. Then, the successive elimination technique is used to solve the inverse of large-scale coefficient matrices of primal-dual systems by more efficient operations on small-scale matrices. In successive elimination, the positive definiteness of several small-scale matrices is used to enhance the numerical stability of computing search directions, and the specific diagonal structures of small-scale matrices are exploited to efficiently compute the search directions. The complexity analysis shows that the efficiency of the proposed method is about one order of magnitude higher than that of the standard IPM. The comparative studies on simulation experiments demonstrate that the MSD-IPM generally outperforms several well-known optimizers (e.g., MOSEK, SDPT3, and SeDuMi) in terms of efficiency and robustness. Finally, the indoor trajectory tracking experiments indicate that the proposed method can generate smooth trajectories for real-world applications.
Highlights
Due to the attractive features in low-cost, maneuverability, flexibility, and hovering-ability, quadrotors are appropriate for various applications including surveillance and reconnaissance, disaster and crisis management, infrastructure inspection, agriculture and forestry, and express delivery [1]
The trajectory planning is formulated as an optimal control problem (OCP), which can be solved by indirect and direct methods [11], [12]
We develop a matrix structure driven interior-point method (MSD-interior point method (IPM)) according to the unique characteristics of quadrotor trajectory planning to improve the computational efficiency
Summary
Due to the attractive features in low-cost, maneuverability, flexibility, and hovering-ability, quadrotors are appropriate for various applications including surveillance and reconnaissance, disaster and crisis management, infrastructure inspection, agriculture and forestry, and express delivery [1]. The trajectory planning is formulated as an optimal control problem (OCP), which can be solved by indirect and direct methods [11], [12]. The efficient convex optimization method [18] have been successfully used to tackle the trajectory planning problem for saving computational cost. In the field of convex-optimization-based quadrotor realtime trajectory planning, Auguglizro et al [28] first proposed a sequential convex programming (SCP) method to enhance the computational efficiency. We develop a matrix structure driven interior-point method (MSD-IPM) according to the unique characteristics of quadrotor trajectory planning to improve the computational efficiency.
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