An efficient method for collision-free and jerk-constrained trajectory generation with sparse desired way-points for a flying robot

In this paper, an efficient approach is developed to plan jerk-constrained smooth trajectories passing through desired way-points with allowable accuracy for an autonomous quadrotor. First, based on the B-spline model, we introduce the sequential convex programming (SCP) into the flexible path planning method to satisfy the way-points constraints. By approximating the quadrotor and obstacles as spheres and directed planes, the length-optimal and collision-free path planning problem is formulated as a nonconvex optimization problem and solved by SCP. The initial C-3 continuous path curve for optimization is constructed efficiently based on a proposed strategy of generating new way-points near the obstacles without the need to calculate the embedding distance between the curve and the obstacles. On this basis, the time-optimal speed planning problem is addressed in two steps. In the first step, the forward-backward approach is introduced to solve the problem under the chord error, velocity, and acceleration constraints by changing the variables and deforming the constraints. Then by relaxing the constraints appropriately, the problem under jerk constraints is formulated into a linear programming (LP) problem. The feasibility of the proposed approach is verified through simulations and an indoor navigation experiment. The proposed approach can generate a C-3 continuous collision-free trajectory that passes through the sparse desired way-points with allowable accuracy while guaranteeing the chord error, velocity, acceleration, and jerk constraints. When the number of sample points is 3000, the proposed speed planning method reduces the calculation time by 40% compared to an existing method.