Path planning is important for the autonomy of Unmanned Aerial Vehicle (UAV), especially for scheduling UAV delivery. However, the operating environment of UAVs is usually uncertain and dynamic. Without proper planning, collisions may happen where multiple UAVs are congested. Besides, there may also be temporary no-fly zone setup by authorities that makes airspace unusable. Thus, proper pre-departure planning that avoids such places is needed. In this paper, we formulate this problem into a Constraint Satisfaction Problem to find a collision-free shortest path on a dynamic graph. We propose a collision-free path planning algorithm that is based on A* algorithm. The main novelty is that we invent a heuristic function that also considers waiting time. We later show that, with added waiting penalty, the proposed algorithm is optimal because the heuristic is admissible. Implementation of this algorithm simulates UAV delivery using Singapore's airspace structure. Our simulation exhibits desirable runtime performance. Using the proposed algorithm, the percentage of collision-free routes decreases as number of requests per unit area increases, and this percentage drops significantly at boundary value. Our empirical analysis could aid the decision-making of no-fly zone policy and infrastructure of UAV delivery.
Off-line algorithms plan the path prior to departure. The aircraft are usually modelled as point mass moving in two dimensions with constant speed and upper-bounded turning rate. @cite_7 uses Genetic Algorithm (GA) to find optimal flyable path through numerous iterations, with each iteration improving previous path by rerouting at waypoint. The problem with Genetic Algorithm is that runtime grows exponentially as number of iterations and flights grows. @cite_5 @cite_2 also uses GA, but with a parallel approach to speedup the calculation. @cite_10 formulates vehicle dynamic model, collision avoidance constraint, and multiple waypoint constraint as mixed-integer linear program (MILP). One of its novelty is that it uses trigonometric functions to better approximate the radius constraint. However, it does not consider battery constraint, which is a limiting factor to UAV's delivery capability. In this paper, we will address both collision avoidance constraint and battery constraint.
@cite_5 @cite_10 @cite_7 @cite_2
2102488278 2587415290 2108400488 2100512461 2748621565 2166194012 2050205301 2341078590 1605218591 2110579257 2031722814 2482392012 2335306738 2772321183 2609088824 2114144879 2729527533 1496280582 2414314951 2112724282
Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance. The formulation can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization. There is extensive literature on using convex optimization to derive piece-wise polynomial trajectories for controlling differential flat systems with applications to three-dimensional flight for Micro Aerial Vehicles. In this work, we propose a method to formulate trajectory generation as a quadratic program (QP) using the concept of a Safe Flight Corridor (SFC). The SFC is a collection of convex overlapping polyhedra that models free space and provides a connected path from the robot to the goal position. We derive an efficient convex decomposition method that builds the SFC from a piece-wise linear skeleton obtained using a fast graph search technique. The SFC provides a set of linear inequality constraints in the QP allowing real-time motion planning. Because the range and field of view of the robot's sensors are limited, we develop a framework of Receding Horizon Planning , which plans trajectories within a finite footprint in the local map, continuously updating the trajectory through a re-planning process. The re-planning process takes between 50 to 300 ms for a large and cluttered map. We show the feasibility of our approach, its completeness and performance, with applications to high-speed flight in both simulated and physical experiments using quadrotors. In the last years, the Flight Mechanics Research Group of Politecnico di Torino started a wide research activity, focused on exploration and implementation of path planning algorithms for commercial autopilots, typically adopted on unmanned vehicles. Different path planning approaches were implemented in a Matlab Simulink based tool, generating waypoints sequences with four methods: geometric predefined trajectories, manual waypoints definition, automatic waypoints distribution (i.e. optimizing camera payload capabilities) and, finally, a comprehensive A*-based approach. The tool was also integrated with functions managing the maps used for planning. In this paper, two approaches to path planning in presence of orographic obstacles are detailed. The first algorithm is subdivided in three phases: the generation of a risk map associated with the ground orography, the transformation of the map in a digraph analyzed with the A* algorithm (to obtain the path with minimum risk minimum distance) and finally the smoothing phase, to obtain a flyable waypoint sequence, realized with the Dubins curves. The structure of this method was defined and implemented, but its optimization is still in progress. The second algorithm is based on the same risk map, but optimizing polynomial curves with a genetic algorithm. This method produces a flyable waypoints sequence, minimizing a cost function reflecting path length and collision risk. An extension of this path solver, including aircraft performance constraints, was also considered. This method was tested on sample domains and its computational cost has still to be evaluated before the implementation in the tool. This paper presents a new approach to trajectory optimization for autonomous fixed-wing aerial vehicles performing large-scale maneuvers. The main result is a planner which designs nearly minimum time planar trajectories to a goal, constrained by no-fly zones and the vehicle's maximum speed and turning rate. Mixed-Integer Linear Programming (MILP) is used for the optimization, and is well suited to trajectory optimization because it can incorporate logical constraints, such as no-fly zone avoidance, and continuous constraints, such as aircraft dynamics. MILP is applied over a receding planning horizon to reduce the computational effort of the planner and to incorporate feedback. In this approach, MILP is used to plan short trajectories that extend towards the goal, but do not necessarily reach it. The cost function accounts for decisions beyond the planning horizon by estimating the time to reach the goal from the plan's end point. This time is estimated by searching a graph representation of the environment. This approach is shown to avoid entrapment behind obstacles, to yield near-optimal performance when comparison with the minimum arrival time found using a fixed horizon controller is possible, and to work consistently on large trajectory optimization problems that are intractable for the fixed horizon controller. This paper studies an unmanned aerial vehicle (UAV)-enabled multicasting system, where a UAV is dispatched to disseminate a common file to a number of geographically distributed ground terminals (GTs). Our objective is to design the UAV trajectory to minimize its mission completion time, while ensuring that each GT is able to successfully recover the file with a high probability required. We consider the use of practical random linear network coding (RLNC) for UAV multicasting, so that each GT is able to recover the file as long as it receives a sufficiently large number of coded packets. However, the formulated UAV trajectory optimization problem is non-convex and difficult to be directly solved. To tackle this issue, we first derive an analytical lower bound for the success probability of each GT's file recovery. Based on this result, we then reformulate the problem into a more tractable form, where the UAV trajectory only needs to be designed to meet a set of constraints each on the minimum connection time with a GT, during which their distance is below a designed threshold. We show that the optimal UAV trajectory only needs to constitute connected line segments, thus it can be obtained by determining first the optimal set of waypoints and then UAV speed along the lines connecting the waypoints. We propose practical schemes for the waypoints design based on a novel concept of virtual base station (VBS) placement and by applying convex optimization techniques. Furthermore, for given set of waypoints, we obtain the optimal UAV speed over the resulting path efficiently by solving a linear programming (LP) problem. Numerical results show that the proposed UAV-enabled multicasting with optimized trajectory design achieves significant performance gains as compared to benchmark schemes. Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work dened a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value. In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as well as the reference trajectory. The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the ecacy of the approach. Genetic Algorithms (GAs) can efficiently produce high quality results for hard combinatorial real world problems such as the Vehicle Routing Problem (VRP). Genetic Vehicle Representation (GVR), a recent approach to solving instances of the VRP with a GA, produces competitive or superior results to the standard benchmark problems. This work extends GVR research by presenting a more precise mathematical model of GVR than in previous works and a thorough comparison of GVR to Path Based Representation approaches. A suite of metrics that measures GVR's efficiency and effectiveness provides an adequate characterization of the jagged search landscape. A new variation of a crossover operator is introduced. A previously unmentioned insight about the convergence rate of the search is also noted that is especially important to the application of a priori and dynamic routing for swarms of Unmanned Aerial Vehicles (UAVs). Results indicate that the search is robust, and it exponentially drives toward high quality solutions in relatively short time. Consequently, a GA with GVR encoding is capable of providing a state-of-the-art engine for a UAV routing system or related application. In this paper we present a model based on the parallel computational tool of cellular automata CA capable of simulating the process of disembarking in a small airplane seat layout, corresponding to Airbus A320 Boeing 737 layout, in search of ways to make it faster and safer under normal evacuation conditions, as well as emergency scenarios. The proposed model is highly customizable, with the number of exits, the walking speed of passengers, depending on their sex, age and height, and the effects of retrieving and carrying luggage. Additionally, the presence of obstacles in the aisles as well as the emergence of panic being parameters whose values can be varied in order to enlighten the disembarking and emergency evacuation processes are considered in detail. The simulation results were compared to existing aircraft disembarking and evacuation times and indicate the efficacy of the proposed model in investigating and revealing passenger attributes during these processes in all the examined cases. Moreover, we parallelized our code in order to run on a graphics processing unit GPU using the CUDA programming language, speeding up the simulation process. Finally, in order to present a fully dynamical anticipative real-time system helpful for decision-making we implemented the proposed CA model in a field programmable gate array FPGA device, and recreated the results given by the software simulations in a fraction of the time. We then compared and exported the performance results among a sequential software implementation, the implementation running on a GPU, and a hardware implementation, proving the consequent acceleration that results from the parallel CA implementation in specific hardware. We present a new approach to the design of smooth trajectories for quadrotor unmanned aerial vehicles (UAVs), which are free of collisions with obstacles along their entire length. To avoid the non-convex constraints normally required for obstacle-avoidance, we perform a mixed-integer optimization in which polynomial trajectories are assigned to convex regions which are known to be obstacle-free. Prior approaches have used the faces of the obstacles themselves to define these convex regions. We instead use IRIS, a recently developed technique for greedy convex segmentation [1], to pre-compute convex regions of safe space. This results in a substantially reduced number of integer variables, which improves the speed with which the optimization can be solved to its global optimum, even for tens or hundreds of obstacle faces. In addition, prior approaches have typically enforced obstacle avoidance at a finite set of sample or knot points. We introduce a technique based on sums-of-squares (SOS) programming that allows us to ensure that the entire piecewise polynomial trajectory is free of collisions using convex constraints. We demonstrate this technique in 2D and in 3D using a dynamical model in the Drake toolbox for Matlab [2]. This paper proposes a novel version of the vehicle routing problem (VRP). Instead of servicing all the customers, feasible solutions of the VRP instance are forced to satisfy a set of complex high-level tasks given as a metric temporal logic (MTL) specification, which allows complex quantitative timing constraints to be incorporated into the problem. For the resulting vehicle routing problem with metric temporal logic specifications (VRPMTL), a mixed-integer linear programming (MILP) based algorithm is provided that solves the problem to optimality. Examples for optimal multi-UAV mission planning are provided where MTL is used as a high level language to specify complex mission tasks. This paper considers the vehicle routing problem with time windows, where the service of each customer must start within a specified time interval. We consider the Lagrangian relaxation of the constraint set requiring that each customer must be served by exactly one vehicle yielding a constrained shortest path subproblem. We present a stabilized cutting-plane algorithm within the framework of linear programming for solving the associated Lagrangian dual problem. This algorithm creates easier constrained shortest path subproblems because less negative cycles are introduced and it leads to faster multiplier convergence due to a stabilization of the dual variables. We have embedded the stabilized cutting-plane algorithm in a branch-and-bound search and introduce strong valid inequalities at the master problem level by Lagrangian relaxation. The result is a Lagrangian branch-and-cut-and-price (LBCP) algorithm for the VRPTW. Making use of this acceleration strategy at the master problem level gives a significant speed-up compared to algorithms in the literature based on traditional column generation. We have solved two test problems introduced in 2001 by Gehring and Homberger with 400 and 1000 customers respectively, which to date are the largest problems ever solved to optimality. We have implemented the LBCP algorithm using the ABACUS open-source framework for solving mixed-integer linear-programs by branch, cut, and price. We explore the challenges of planning trajectories for quadrotors through cluttered indoor environments. We extend the existing work on polynomial trajectory generation by presenting a method of jointly optimizing polynomial path segments in an unconstrained quadratic program that is numerically stable for high-order polynomials and large numbers of segments, and is easily formulated for efficient sparse computation. We also present a technique for automatically selecting the amount of time allocated to each segment, and hence the quadrotor speeds along the path, as a function of a single parameter determining aggressiveness, subject to actuator constraints. The use of polynomial trajectories, coupled with the differentially flat representation of the quadrotor, eliminates the need for computationally intensive sampling and simulation in the high dimensional state space of the vehicle during motion planning. Our approach generates high-quality trajecrtories much faster than purely sampling-based optimal kinodynamic planning methods, but sacrifices the guarantee of asymptotic convergence to the global optimum that those methods provide. We demonstrate the performance of our algorithm by efficiently generating trajectories through challenging indoor spaces and successfully traversing them at speeds up to 8 m s. A demonstration of our algorithm and flight performance is available at: http: groups.csail.mit.edu rrg quad_polynomial_trajectory_planning. The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal control problem is typically computationally expensive and infeasible for real-time trajectory planning. This paper presents an iterative algorithm that divides the path generation task into two sequential subproblems that are significantly easier to solve. Given an initial path through the race track, the algorithm runs a forward-backward integration scheme to determine the minimum-time longitudinal speed profile, subject to tire friction constraints. With this fixed speed profile, the algorithm updates the vehicle's path by solving a convex optimization problem that minimizes the resulting path curvature while staying within track boundaries and obeying affine, time-varying vehicle dynamics constraints. This two-step process is repeated iteratively until the predicted lap time no longer improves. While providing no guarantees of convergence or a globally optimal solution, the approach performs very well when validated on the Thunderhill Raceway course in Willows, CA. The predicted lap time converges after four to five iterations, with each iteration over the full 4.5 km race course requiring only thirty seconds of computation time on a laptop computer. The resulting trajectory is experimentally driven at the race circuit with an autonomous Audi TTS test vehicle, and the resulting lap time and racing line is comparable to both a nonlinear gradient descent solution and a trajectory recorded from a professional racecar driver. The experimental results indicate that the proposed method is a viable option for online trajectory planning in the near future. Quadrotors that navigate through unknown, cluttered environments have only recently begun to emerge following the development of small form-factor sensing and computing hardware and computationally efficient collision avoidance algorithms. Computation time of planning algorithms has significantly decreased in part to using local information as opposed to using a global map for collision avoidance. Safe planning with local information, however, restricts the direction of travel to remain within the perception system's field-of-view (FOV). The vehicle's motion becomes more constrained with body-mounted narrow FOV sensors, reducing vehicle maneuverability and speed. This work presents a relaxed-constraint Model Predictive Control framework that allows motions outside the perception FOV with guaranteed safety. The key aspect of this approach is the ability to safely choose a motion primitive generated in the past. Simulation and hardware results shows the new framework improves time to goal and flight path efficiency in environments with varying levels of clutter. Introduce a new time-dependent UAV heterogeneous fleet routing problem.Consider several objective functions and respect drones operational requirements.Design a MILP model in order to find sets of non-dominated solutions.Consider a model able to tackle multi-layer scenarios with package exchanging points.Integrate UAV into the new concepts of mini microgrid systems inside smart cities. This paper introduces an Unmanned Aerial Vehicle (UAV) heterogeneous fleet routing problem, dealing with vehicles limited autonomy by considering multiple charging stations and respecting operational requirements. A green routing problem is designed for overcoming difficulties that exist as a result of limited vehicle driving range. Due to the large amount of drones emerging in the society, UAVs use and efficiency should be optimized. In particular, these kinds of vehicles have been recently used for delivering and collecting products. Here, we design a new real-time routing problem, in which different types of drones can collect and deliver packages. These aerial vehicles are able to collect more than one deliverable at the same time if it fits their maximum capacity. Inspired by a multi-criteria view of real systems, seven different objective functions are considered and sought to be minimized using a Mixed-Integer Linear Programming (MILP) model solved by a matheuristic algorithm. The latter filters the non-dominated solutions from the pool of solutions found in the branch-and-bound optimization tree, using a black-box dynamic search algorithm. A case of study, considering a bi-layer scenario, is presented in order to validate the proposal, which showed to be able to provide good quality solutions for supporting decision making. In this paper, we study the problem of optimal trajectory generation for a team of heterogeneous robots moving in a plane and tracking a moving target by processing relative observations, i.e., distance and or bearing. Contrary to previous approaches, we explicitly consider limits on the robots' speed and impose constraints on the minimum distance at which the robots are allowed to approach the target. We first address the case of a single tracking sensor and seek the next sensing location in order to minimize the uncertainty about the target's position. We show that although the corresponding optimization problem involves a nonconvex objective function and a nonconvex constraint, its global optimal solution can be determined analytically. We then extend the approach to the case of multiple sensors and propose an iterative algorithm, i.e., the Gauss-Seidel relaxation (GSR), to determine the next best sensing location for each sensor. Extensive simulation results demonstrate that the GSR algorithm, whose computational complexity is linear in the number of sensors, achieves higher tracking accuracy than gradient descent methods and has performance that is indistinguishable from that of a grid-based exhaustive search, whose cost is exponential in the number of sensors. Finally, through experiments, we demonstrate that the proposed GSR algorithm is robust and applicable to real systems. The current boom of Unmanned Aerial Vehicles (UAVs) is increasing the number of potential industrial and research applications. One of the most demanded topics in this area is related to the automated planning of a UAVs swarm, controlled by one or several Ground Control Stations (GCSs). In this context, there are several variables that influence the selection of the most appropriate plan, such as the makespan, the cost or the risk of the mission. This problem can be seen as a Multi-Objective Optimization Problem (MOP). On previous approaches, the problem was modelled as a Constraint Satisfaction Problem (CSP) and solved using a Multi-Objective Genetic Algorithm (MOGA), so a Pareto Optimal Frontier (POF) was obtained. The main problem with this approach is based on the large number of obtained solutions, which hinders the selection of the best solution. This paper presents a new algorithm that has been designed to obtain the most significant solutions in the POF. This approach is based on Knee Points applied to MOGA. The new algorithm has been proved in a real scenario with different number of optimization variables, the experimental results show a significant improvement of the algorithm performance. Unmanned Systems has been taking place of manned systems in several fields like aviation. Unmanned Aerial Vehicle (UAV), one of the most popular and effective unmanned systems, is gradually becoming the vital element of aviation because of its high success rate in both military and civilian missions. Basic problem of UAV is finding the best path in tough environment. Coverage zones of radars and complex environment are the main obstacles in this problem. A UAV intends to travel all control points in an optimal way to be more productive while avoiding radars. In this paper, we used Genetic Algorithm (GA), which is Evolutionary algorithm, to find the optimal flyable path for the UAVs in a 3D environment. Each generation is anticipated to be better than its previous generation in GA. For the purpose of reaching an optimal path, solving the Travelling Salesman Problem (TSP) is one of the major phases in the proposed method. In order to show the visual of solution in better quality, we preferred MATLAB as the implementation environment. Additionally, there is a shared library and mathematical calculations are easier in MATLAB. The complexity of our problem can be increased by adding extra constraints caused by the dynamic environment as the future works. Experimental results show that GA can be opted for optimal path planning for the UAVs. We present an online method for generating collision-free trajectories for autonomous quadrotor flight through cluttered environments. We consider the real-world scenario that the quadrotor aerial robot is equipped with limited sensing and operates in initially unknown environments. During flight, an octree-based environment representation is incrementally built using onboard sensors. Utilizing efficient operations in the octree data structure, we are able to generate free-space flight corridors consisting of large overlapping 3-D grids in an online fashion. A novel optimization-based method then generates smooth trajectories that both are bounded entirely within the safe flight corridor and satisfy higher order dynamical constraints. Our method computes valid trajectories within fractions of a second on a moderately fast computer, thus permitting online re-generation of trajectories for reaction to new obstacles. We build a complete quadrotor testbed with onboard sensing, state estimation, mapping, and control, and integrate the proposed method to show online navigation through complex unknown environments. This paper proposes a genetic algorithm (GA) for path planning of an autonomous underwater vehicle in an ocean environment characterized by strong currents and enhanced space-time variability. The goal is to find a safe path that takes the vehicle from its starting location to a mission-specified destination, minimizing the energy cost. The GA includes novel genetic operators that ensure the convergence to the global minimum even in cases where the structure (in space and time) of the current field implies the existence of different local minima. The performance of these operators is discussed. The proposed algorithm is suitable for situations in which the vehicle has to operate energy-exhaustive missions.