TimeOptimal Trajectory Generation for Dynamic Vehicles: A Bilevel Optimization Approach This paper presents a general framework to find timeoptimal trajectories for dynamic vehicles like drones and autonomous cars. Hindered by its nonlinear objective and complex constraints, this problem is hard even for stateof theart nonlinear programming (NLP) solvers. The proposed framework addresses the problem by bilevel optimization. Specifically, the original problem is divided into an inner layer, which computes a timeoptimal velocity profile along a fixed geometric path, and an outer layer, which refines the geometric path by a QuasiNewton method. The inner optimization is convex and efficiently solved by interiorpoint methods. A novel variable reordering method is introduced to accelerate the optimization of the velocity profile. The gradients of the outer layer can be derived from the Lagrange multipliers using sensitivity analysis of parametric optimization problems. The method is guaranteed to return a feasible solution at any time, and numerical experiments on a ground vehicle with friction circle dynamics model show that the proposed method performs more robustly than general NLP solvers.

ALTRO: A Fast Solver for Constrained Trajectory Optimization Trajectory optimization is a widely used tool for robot motion planning and control. Existing solvers for these problems either rely on offtheshelf nonlinear programming solvers that are numerically robust and capable of handling arbitrary constraints, but tend to be slow because they are general purpose; or they use custom numerical methods that take advantage of the problem structure to be fast, but often lack robustness and have limited or no ability to reason about constraints. This paper presents ALTRO (Augmented Lagrangian TRajectory optimizer), a solver for constrained trajectory optimization problems that handles general nonlinear state and input constraints and offers fast convergence and numerical robustness thanks to careful exploitation of problem structure. We demonstrate its performance on a set of benchmark motionplanning problems and offer comparisons to the standard direct collocation method with largescale sequential quadratic programming and interiorpoint solvers.