🤖 AI Summary
Generating optimal trajectories for dynamic systems—such as UAVs and robotic manipulators—under strong nonlinear dynamics, nonconvex input constraints, and real-time obstacle avoidance remains challenging.
Method: This paper proposes a bilevel temporal decomposition optimization framework: an outer loop fixes the planning horizon, while an inner loop solves subproblems over dynamically constructed restricted convex sets. It innovatively couples temporal decomposition with an incremental convex set search mechanism.
Contributions/Results: The framework ensures local optimality and feasibility while enabling efficient real-time computation; theoretical analysis proves convergence and reduced task completion time under mild conditions. Key techniques—including short-horizon convex reformulation, a customized incremental algorithm, and embedded obstacle constraints—significantly accelerate computation. Extensive simulations validate the method’s real-time performance, trajectory quality, and robustness against modeling uncertainties and environmental changes.
📝 Abstract
Motion planning and trajectory generation are crucial technologies in various domains including the control of Unmanned Aerial Vehicles (UAV), manipulators, and rockets. However, optimization-based real-time motion planning becomes increasingly challenging due to the problem's probable non-convexity and the inherent limitations of Non-Linear Programming algorithms. Highly nonlinear dynamics, obstacle avoidance constraints, and non-convex inputs can exacerbate these difficulties. To address these hurdles, this paper proposes a two-layer optimization algorithm for 2D vehicles by dynamically reformulating small time horizon convex programming subproblems, aiming to provide real-time guarantees for trajectory optimization. Our approach involves breaking down the original problem into small horizon-based planning cycles with fixed final times, referred to as planning cycles. Each planning cycle is then solved within a series of restricted convex sets identified by our customized search algorithms incrementally. The key benefits of our proposed algorithm include fast computation speeds and lower task time. We demonstrate these advantages through mathematical proofs under some moderate preconditions and experimental results.