SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS： IMPLEMENTATION AND COMPUTATIONAL RESULTS

In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

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.

Efficient optimization method for variable-specific-impulse low-thrust trajectories with shutdown constraint

This paper develops a sequential convex programming(SCP)-based method to solve the minimum-fuel variable-specific-impulse low-thrust transfer problem considering shutdown constraint,with emphasize on improving the computational efficiency.The variable parameter engine is more applicable for many low-thrust scenarios,therefore,both a continuously variable model and a ladder variable model are adopted.First,the original problem is convexified by processing the constraint feasible domain,which is composed of the nonlinear dynamic equations and second-order equality constraint,into convex sets.Then,the approximation is generated to close the optimal solution of the low-thrust problem by iteratively solving the convexified subproblem.Moreover,the switching self-detection and adaptive node refinement methods are presented,which can improve the accuracy of the solution and accelerate the convergence during the approximation process and is especially necessary and effective in the scenarios with shutdown constraint.In numerical simulations,the comparison with the homotopic approach shows that the proposed method only needs 4%computational time as that of the homotopic approach,and two variable-specificimpulse examples further demonstrate the effectiveness and efficiency of the proposed method.