Flight Trajectory Optimization Techniques

Researchers at Hong Kong University MaRS Lab have just published another jaw dropping paper featuring their safety-assured high-speed aerial robot path planning system dubbed "SUPER". With a single MID360 lidar sensor they repeatedly achieved autonomous one-shot navigation at speeds exceeding 20m/s in obstacle rich environments. Since it only requires a single lidar these vehicles can be built with a small footprint and navigate completely independent of light, GPS and radio link. This is not just #SLAM on a #drone, in fact the SUPER system continuously computes two trajectories in each re-planning cycle—a high-speed exploratory trajectory and a conservative backup trajectory. The exploratory trajectory is designed to maximize speed by considering both known free spaces and unknown areas, allowing the drone to fly aggressively and efficiently toward its goal. In contrast, the backup trajectory is entirely confined within the known free spaces identified by the point-cloud map, ensuring that if unforeseen obstacles are encountered or if the system’s perception becomes uncertain, the system can safely switch to a precomputed, collision-free path. The direct use of LIDAR point clouds for mapping eliminates the need for time-consuming occupancy grid updates and complex data fusion algorithms. Combined with an efficient dual-trajectory planning framework, this leads to significant reductions in computation time—often an order of magnitude faster than comparable SLAM-based systems—allowing the MAV to operate at higher speeds without sacrificing safety. This two-pronged planning strategy is particularly innovative because it directly addresses the classic speed-safety trade-off in autonomous navigation. By planning an exploratory trajectory that pushes the speed envelope and a backup trajectory that guarantees safety, SUPER can achieve high-speed flight (demonstrated speeds exceeding 20 meters per second) without compromising on collision avoidance. If you've been tracking the progress of autonomy in aerial robotics and matching it to the winning strategies emerging in Ukraine, it's clear we're likely to experience another ChatGPT moment in this domain, very soon. #LiDAR scanners will continue to get smaller and cheaper, solid state VSCEL based sensors are rapidly improving and it is conceivable that vehicles with this capability can be built and deployed with a bill of materials below $1000. Link to the paper in the comments below.

As part of my recent research, I developed and simulated an optimized lunar transfer trajectory from Low Earth Orbit (LEO) for a flyby mission using MATLAB. This work is designed to support researchers and commercial actors exploring efficient, low-cost lunar missions, especially within the complex dynamics of the 3-body Earth-Moon-spacecraft system. 💡 What is a flyby mission? It’s a gravity-assist trajectory where the spacecraft swings by celestial bodies in this case, Earth and Moon using their gravity to change its path without major maneuvers beyond the initial escape burn. This significantly saves fuel and energy. ✅ What did My optimization achieve? 1- Reduced ΔV required for the Trans-Lunar Injection (TLI) from 3.1125 → 2.8685 km/s 2- ~860 kg of fuel saved 3- Higher maneuver efficiency and sustainable trajectory stability 📊 Summary of Results 🔸 Before Optimization: ΔV used: 3.1125 km/s Fuel used: 18,420.91 kg Efficiency: 63.96% 🔸 After Optimization: Optimal flight path angle: 0.97004 ΔV reduced to: 2.8685 km/s Fuel used: 17,556.70 kg Fuel saved: ~864.2 kg Efficiency: 60.96% 📈 What's inside the project? - Full mathematical model development - Optimization algorithms - Visual analysis & plots - Full references for further reading 🛰 What's next? I’m currently looking to validate these results using real mission data or existing TLI profiles. If you’re aware of open datasets, spacecraft telemetry, or platforms for simulating translunar trajectories, I’d love to connect and collaborate. If you or your team work on lunar navigation, trajectory validation, or mission planning, let’s talk! #SpaceExploration #TrajectoryDesign #MATLAB #FlybyMission #Astrodynamics #MoonMission #Optimization #TLI

QUAV: Quantum-Assisted Path Planning and Optimization for UAV Navigation with Obstacle Avoidance by New York University Abu Dhabi & Thales by Nouhaila I., Muhammad Kashif, Alberto Marchisio, Yung-Sze Gan, Frédéric Barbaresco , Muhammad Shafique https://lnkd.in/eiQZUnBN Abstract The growing demand for drone navigation in urban and restricted airspaces requires real-time path planning that is both safe and scalable. Classical methods often struggle with the computational load of high-dimensional optimization under dynamic constraints like obstacle avoidance and no-fly zones. This work introduces QUAV, a quantum-assisted UAV path planning framework based on the Quantum Approximate Optimization Algorithm (QAOA), to the best of our knowledge, this is one of the first applications of QAOA for drone trajectory optimization. QUAV models pathfinding as a quantum optimization problem, allowing efficient exploration of multiple paths while incorporating obstacle constraints and geospatial accuracy through UTM coordinate transformation. A theoretical analysis shows that QUAV achieves linear scaling in circuit depth relative to the number of edges, under fixed optimization settings. Extensive simulations and a realhardware implementation on IBM’s ibm_kyiv backend validate its performance and robustness under noise. Despite hardware constraints, results demonstrate that QUAV generates feasible, efficient trajectories, highlighting the promise of quantum approaches for future drone navigation systems.

TRUST-Planner: Topology-guided Robust Trajectory Planner for AAVs with Uncertain Obstacle Spatial-temporal Avoidance Arxiv: https://lnkd.in/ezRgJgDc Video (not this paper): https://lnkd.in/eA4FDdwh How can Autonomous Aerial Vehicles (AAVs) safely navigate dense, dynamic environments where obstacles move unpredictably? TRUST-Planner introduces a topology-guided hierarchical framework that integrates global topological exploration with predictive, lightweight trajectory optimization—achieving 96% success rates in simulation and millisecond-level replanning in real-world flights. 🔁 At a Glance 💡 Goal: Overcome local minima, deadlocks, and collisions in dynamic AAV navigation by combining spatial-temporal topology guidance with robust trajectory optimization. ⚙️ Approach: Frontend (DEV-PRM): Dynamic Enhanced Visible Probabilistic Roadmap for diverse topological path exploration. Backend (UTF-MINCO): Uniform terminal-free minimum control polynomial + Dynamic Distance Field for predictive obstacle avoidance. Multi-branch Management: Incremental, parallel trajectory updates maintain multiple safe alternatives in real time. 📈 Impact (Key Metrics) 🧪 Simulation +81.9% efficiency in topological search vs. V-PRM. 96% success rate in cluttered, dynamic environments. Millisecond-level optimization (10 ms average per trajectory). 🤖 Real-World (Crazyflie 2.1 Nano Drone) Robust flights in static, dynamic, and adversarial penetration scenarios. Drone maintains near-max speed while avoiding multiple moving obstacles. 🔬 Experiments 🧪 Environments: Randomized static + dynamic obstacle fields, indoor motion capture trials. 🎯 Tasks: Navigation, obstacle avoidance, penetration through interceptors. 🦾 Robot: Crazyflie 2.1 with OptiTrack-based localization. 📐 Input: Position + velocity estimates of obstacles (EKF). 🛠 How to Implement 1️⃣ DEV-PRM Frontend – Uses Predictive Directional Cones + obstacle-aware sampling to capture spatio-temporal topology. 2️⃣ UTF-MINCO Backend – Lightweight unconstrained optimization with relaxed terminals + analytical gradients. 3️⃣ Incremental Multi-branch Framework – Parallel updating of main + alternative trajectories for real-time safety. 📦 Deployment Benefits ✅ Breaks out of local minima & deadlocks with multi-topology planning. ✅ Millisecond-level replanning for dynamic obstacle fields. ✅ Provides multiple safe fallback trajectories. ✅ Applicable to drones, autonomous vehicles, and dynamic robotics domains. Takeaway TRUST-Planner redefines AAV trajectory planning: not just finding a path, but managing diverse, safe futures in real time. Its blend of topology guidance + predictive optimization sets a new benchmark for robust aerial autonomy. Follow me to know more about AI, ML and Robotics!

A SHORT COURSE on INTELLIGENT FLIGHT CONTROL, Part 7 Dynamic Optimization -------------------------------------------- Methods of static optimization considered in Parts 5 and 6 can be extended to an aircraft's dynamic systems by minimizing a SCALAR COST FUNCTION, J. Dynamic systems are described by a vector differential equation relating the RATE-OF-CHANGE of the state vector to a function of the state, control, and disturbance vectors (x,u,w). J is the scalar time-integral of a cost function, L(x,t), and the system equation, x(t)_dot – f[x(t),u(t)] = 0. The system equation is adjoined to L(.) by a Lagrange multiplier vector, lambda (t), in the integrand of J. For NONLINEAR SYSTEMS, the optimization methods described in Part 6 can be adapted to minimize J, producing a control history u(t) that generates an optimal trajectory and satisfies an end condition, Phi[x(t_f)]. For the SPECIAL CASE of linear system equations, either time-invariant or time-varying (LTI, LTV), the optimal solution can be expressed as a LINEAR FEEDBACK CONTROL LAW, u(t) = -C(t) x(t). The LTV C(t) is a function of an intermediate matrix S(t). S(t) is the solution of a differential equation called the MATRIX RICCATI EQUATION. The Riccati equation is coupled to the system dynamic equation, assuring that the cost is minimized subject to the dynamic constraint. For the LTI case, S(t)_dot = 0, and the differential equation reduces to an ALGEBRAIC EQUATION. The closed-loop system is guaranteed to be STABLE even if the open-loop system is unstable, subject to requirements summarized in the referenced slide set. Recent advances in dynamic optimization are made possible by new algorithms and increases in computer speed and memory. Techniques include MACHINE LEARNING, PHYSICS-BASED NEURAL NETWORKS, EVOLUTIONARY ALGORITHMS, MODEL PREDICTIVE CONTROL, and LARGE-SCALE SOLVERS. ----- Reference . https://lnkd.in/em5cmGii. . Google AI Overview of Recent Advances in Dynamic Optimization, (see addendum below the graphic) . Reinforcement Learning, https://lnkd.in/eTENQjqw . Physics Informed Neural Networks, https://lnkd.in/ePweQSMk . Evolutionary Algorithms, https://lnkd.in/eneEjyRm . Model Predictive Control, https://lnkd.in/ebFUJykt . Parts 1 to 6 in previous LinkedIn posts =====

Our paper "Routing a fleet of unmanned aerial vehicles: A trajectory optimisation-based framework", co-authored with Walton P. Coutinho, Joerg Fliege, and Maria Battarra, has just been published in Transportation Research Part B: Methodological! Main contributions: 🎯 We propose a novel multi-phase Mixed-Integer Nonlinear Programming formulation for the Glider Routing and Trajectory Optimisation (TO) Problem (GRTOP) that allows for the use of sub-models of varying fidelity for TO. For example, along the arcs of a given route, we allow for distinct flight modes, flight dynamics, wind conditions, discretisation methods and discretisation step sizes. 🎯 We provide theoretical bounds on the discretisation errors for the linearised reformulation of the gliders’ Equations of Motion and demonstrate how to reformulate the proposed GRTOP model to include the error-bounding constraints. Our experiments show that providing a modelling framework that incorporates such errors leads to more accurate trajectories. 🎯 We develop two heuristics based on the so-called STO approach, designed to find feasible (flyable) trajectories for a given route with low computational effort. The first heuristic is based on non-convex trajectory optimisation subproblems, while the second one is based on an iterative flight time minimisation procedure that solves Second-Order Cone Programming subproblems. 🎯 By integrating the proposed STO heuristics with a state-of-the-art routing algorithm, we develop a new matheuristic framework for the GRTOP in which we decouple the continuous dynamics of flight from the combinatorial waypoint routing problem. We highlight that such integration is non-trivial since one has to find a good compromise between local search and trajectory computations to develop a scalable algorithm. This computational framework allows us to solve large-sized problem instances. This article is derived from Walton's PhD work (concluded in 2018) at the University of Southampton, supervised by Jörg and Maria. It took a while for us to converge on a nice publication, but the day has come, thanks to Walton's persistence. Link for the paper: https://lnkd.in/diKKp8dh Walton is originally from Timbaúba, Pernambuco, and is now a faculty member at the Universidade Federal de Pernambuco. I had the opportunity to co-advise his excellent master’s work on the Close-Enough TSP at the Universidade Federal da Paraíba alongside Roberto Quirino Nascimento, with outstanding collaboration from Artur Pessoa. This led to a publication in the INFORMS Journal on Computing: https://lnkd.in/ddpM7bAT. I first met Walton in 2011, when he was my teaching assistant in an OR course. He saved me at the time by developing excellent slides and helping me prepare engaging classes. That year, he told me he dreamed of obtaining a PhD in the UK, and I am grateful to Maria, Jörg, and CNPq for helping him achieve that dream seven years later. Well done, Walton!

Would the evolution of Flight Management Systems be AI-Adaptive ? The Flight Management System (FMS) is one of the key and most developed modern avionics systems —integrating navigation, performance, and guidance. Traditionally, FMS architectures have been deterministic, relying on static aerodynamic models and predefined performance tables. This limits optimization under evolving flight conditions such as atmospheric variations, engine wear, and ATC constraints [1]. Artificial Intelligence (AI) introduces adaptive optimization. Machine learning algorithms trained on historical and live flight data can refine predictions beyond certified nominal baselines [2]. FMS AI-driven capabilities might include: • Real-Time Trajectory Adaptation Reinforcement learning updates flight policies to minimize fuel, time, and airspace costs, dynamically responding to winds, traffic, and reroutes [2] • Predictive Performance Modeling Bayesian inference and recurrent neural networks (RNNs) infer updated drag polars and thrust-specific fuel consumption (TSFC) variations due to engine degradation or environmental changes, correcting fuel flow and range predictions [2]. • Intelligent Decision Support Explainable AI (XAI) ensures adaptive algorithms remain transparent, allowing pilots to validate trajectory or cost index adjustments [2]. For example, an AI-based adaptive cost index could be be expressed as: CI(t) = CT(t) / CF(t) = (β * t_dot(t)) / (α * m_dot_f(t) * p_f(t)) Where: CI(t) = adaptive cost index m_dot_f(t) = real-time fuel flow p_f(t) = instantaneous fuel price or energy cost factor t_dot(t) = time variation due to trajectory updates α, β = AI-learned weighting coefficients [2] This allows continuous balancing of fuel and time costs, turning FMS into a self-optimizing agent integrating performance, economics, and airspace constraints. Such architectures align with Trajectory-Based Operations (TBO), where aircraft exchange predicted trajectories with ATC and AOC systems to enhance network efficiency [1]. However, certification remains a challenge. Compliance with DO-178C / DO-330 for adaptive learning requires traceability and explainability—a paradigm shift for avionics [3]. NASA’s Learn-to-Fly demonstrates progress toward certifiable autonomy using hybrid physics-AI models [2]. The next-generations FMS would evolve from a deterministic planner into a cognitive, adaptive co-pilot, learning, predicting, and collaborating across a connected aviation ecosystem. Just food for thoughts… Do you believe adaptive learning could ever be certifiable in commercial avionics—or will regulation always limit the FMS to deterministic logic? References [1] SESAR, Trajectory-Based Operations Concept https://lnkd.in/d4BnJe6C [2] NASA, Learn-to-Fly: Adaptive Flight Control and Model Learning https://lnkd.in/dNbk3Ctp [3] RTCA, DO-178C / DO-330. https://lnkd.in/dY_rA9WX #FlightManagementSystem #AIinAviation #MachineLearning #Avionics #Boeing #RAeS

🎯 Control Theory Example: Minimum-Energy Rocket Steering Goal: Steer a rocket from point A to point B using the least energy, subject to dynamic constraints. 📐 State-Space Dynamics Let: x(t) ∈ ℝ² → rocket position v(t) ∈ ℝ² → rocket velocity u(t) ∈ ℝ² → control (thrust acceleration), with ‖u(t)‖ ≤ uₘₐₓ Dynamics: dx/dt = v dv/dt = u 🧮 Objective: Minimize Energy Cost functional: J = ∫₀ᵀ ‖u(t)‖² dt 🔧 Hamiltonian (Pontryagin Form) Introduce costate variables: λₓ(t) → conjugate to x(t) λᵥ(t) → conjugate to v(t) Hamiltonian: H = λₓᵀ·v + λᵥᵀ·u + ‖u‖² Minimization condition: ∂H/∂u = λᵥ + 2u = 0 ⇒ u* = –½ λᵥ 🧠 Interpretation The optimal control is proportional to the negative of the costate λᵥ. Costate evolution equations: dλₓ/dt = –∂H/∂x = 0 dλᵥ/dt = –∂H/∂v = –λₓ → This is a Hamiltonian system: the state and costate evolve in coupled pairs. 📈 Applications Energy-efficient robot arm motion Autonomous vehicle trajectory planning Satellite orbit transfer optimization Economic models with capital and cost dynamics ⛔ Caution with the infographics #ControlTheory #Hamiltonian #OptimalControl #Pontryagin #RocketScience #TrajectoryOptimization #AppliedMathematics #SystemDynamics #EngineeringControl #Robotics #MathematicalModeling