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
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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. In recent years, Unmanned Aerial Vehicles (UAVs) have been used in many military and civil application areas, due to their increased endurance, performance, portability, and their larger payload-carrying, computing and communication capabilities. Because of UAVs' complex operation areas and complicated constraints related to the assigned task, they have to fly on a path, which is calculated online and or offline to satisfy these constraints and to check some control points in the operation theatre. If the number of control points and constraints increases, finding a feasible solution takes up too much time in this large operation area. In this case, the use of multi-UAVs decreases operation completion time; however, this usage increases the complexity of finding a feasible path problem. This problem is typically NP-hard and genetic algorithms have been successfully utilized for solving it in the last few decades. This paper presents how a flyable trajectory can be constructed for multi-UAV systems by using a Genetic Algorithm (GA) in a known environment and at a constant altitude. A GA is implemented parallel in a multi-core environment to increase the performance of the system. First, a feasible path is calculated by using a parallel GA, and then the path is smoothed by using Bezier curves to convert it flyable. Preliminary results show that the proposed method provides an effective and feasible path for each UAV in an Unmanned Aerial System with multi-UAVs. The proposed system is realized in Java with a GUI for showing results. This paper also outlines future work that can be conducted on the multi-UAV path planning. 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. 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. The goal of adaptive sampling in the ocean is to predict the types and locations of additional ocean measurements that would be most useful to collect. Quantitatively, what is most useful is defined by an objective function and the goal is then to optimize this objective under the constraints of the available observing network. Examples of objectives are better oceanic understanding, to improve forecast quality, or to sample regions of high interest. This work provides a new path-planning scheme for the adaptive sampling problem. We define the path-planning problem in terms of an optimization framework and propose a method based on mixed integer linear programming (MILP). The mathematical goal is to find the vehicle path that maximizes the line integral of the uncertainty of field estimates along this path. Sampling this path can improve the accuracy of the field estimates the most. While achieving this objective, several constraints must be satisfied and are implemented. They relate to vehicle motion, intervehicle coordination, communication, collision avoidance, etc. The MILP formulation is quite powerful to handle different problem constraints and flexible enough to allow easy extensions of the problem. The formulation covers single- and multiple-vehicle cases as well as single- and multiple-day formulations. The need for a multiple-day formulation arises when the ocean sampling mission is optimized for several days ahead. We first introduce the details of the formulation, then elaborate on the objective function and constraints, and finally, present a varied set of examples to illustrate the applicability of the proposed method. Unmanned Aerial Vehicles (UAVs) are used in numerous military and civil application areas, and they have gained prominence in the research community. A UAV has to operate in a complex environment and checks the control points in the mission area by satisfying different constraints of the assigned task. Therefore, the path planning problem is one of the important areas in UAV researches. If the number of control points increases in the Unmanned Aerial System (UAS), finding a feasible solution in this large search space takes up a great deal of time. Nowadays low-cost UAVs are available, and this enables the use of multi-UAV systems to perform different tasks more efficiently and quickly. This usage increases the complexity of effective path planning and task allocation problem. This paper presents a flyable path planning for multi-UAV systems by using a Genetic Algorithm (GA) in a known environment at a constant altitude. A feasible path is firstly calculated by GAs, and then this path is smoothed by using Bezier curves. Experimental results indicate that the proposed approach produces effective and feasible paths for each UAV in a multi-UAV system. System is implemented in Java with a GUI for presenting results. The paper also draws future works that can be done on this topic. Abstract The main goal of this research effort is to find a flyable collision-free path for an unmanned aerial vehicle (UAV) in a dynamic environment. Given that the UAV path planning needs to adapt in near real-time to the dynamic nature of the operational scenario, and to react rapidly to updates in the situational awareness, a modified artificial potential field (MAPF) approach is utilized to provide collision avoidance in view of pop-up threats and a random set of moving obstacles. To ensure a practically reachable trajectory, this paper proposes a constraint reference frame to develop MAPF so that the decomposed forces from MAPF can be matched with the physical constraints of the UAV for online adjustment. Simulations and experimental results provide promising validation in terms of the efficiency and scalability of the proposed approach. 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. 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]. The initial state of an Unmanned Aerial Vehicle (UAV) system and the relative state of the system, the continuous inputs of each flight unit are piecewise linear by a Control Parameterization and Time Discretization (CPTD) method. The approximation piecewise linearization control inputs are used to substitute for the continuous inputs. In this way, the multi-UAV formation reconfiguration problem can be formulated as an optimal control problem with dynamical and algebraic constraints. With strict constraints and mutual interference, the multi-UAV formation reconfiguration in 3-D space is a complicated problem. The recent boom of bio-inspired algorithms has attracted many researchers to the field of applying such intelligent approaches to complicated optimization problems in multi-UAVs. In this paper, a Hybrid Particle Swarm Optimization and Genetic Algorithm (HPSOGA) is proposed to solve the multi-UAV formation reconfiguration problem, which is modeled as a parameter optimization problem. This new approach combines the advantages of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), which can find the time-optimal solutions simultaneously. The proposed HPSOGA will also be compared with basic PSO algorithm and the series of experimental results will show that our HPSOGA outperforms PSO in solving multi-UAV formation reconfiguration problem under complicated environments. When controlling dynamic systems, such as mobile robots in uncertain environments, there is a trade off between risk and reward. For example, a race car can turn a corner faster by taking a more challenging path. This paper proposes a new approach to planning a control sequence with a guaranteed risk bound. Given a stochastic dynamic model, the problem is to find a control sequence that optimizes a performance metric, while satisfying chance constraints i.e. constraints on the upper bound of the probability of failure. We propose a two-stage optimization approach, with the upper stage optimizing the risk allocation and the lower stage calculating the optimal control sequence that maximizes reward. In general, the upper-stage is a non-convex optimization problem, which is hard to solve. We develop a new iterative algorithm for this stage that efficiently computes the risk allocation with a small penalty to optimality. The algorithm is implemented and tested on the autonomous underwater vehicle (AUV) depth planning problem, and demonstrates a substantial improvement in computation cost and suboptimality, compared to the prior arts. The optimal multiple multicast problem (OMMP) on wavelength division multiplexing ring networks without wavelength conversion is considered in this paper. When the physical network and the set of multicast requests are given, OMMP is the problem that selects a suitable path or (paths) and wavelength (or wavelengths) among the many possible choices for each multicast request under the constraint that not any paths using the same wavelength pass through the same link such that the number of used wavelengths is minimized. This problem can be proven to be NP-hard. In the paper, a formulation of OMMP is given and several genetic algorithms (GAs) are proposed to solve it. Experimental results indicate that the proposed GAs are robust for this problem. 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. We present a parallel Cartesian planning algorithm for redundant robot arms and manipulators. We pre-compute a roadmap, that takes into account static obstacles in the environment as well as singular configurations. At runtime, multiple paths in this roadmap are computed as initial trajectories for an optimization-based planner that tends to satisfy various constraints corresponding to demands on the trajectory, including end-effector constraints, collision-free, and non-singular. We highlight and compare the performance of our parallel planner using 7-DOF arms with other planning algorithms. To the best of our knowledge, this is the first approach that can compute smooth and collision-free trajectories in complex environments with dynamic obstacles. Existing approaches to multirobot coordination separate scheduling and task allocation, but finding the optimal schedule with joint tasks and spatial constraints requires robots to simultaneously solve the scheduling, task allocation, and path planning problems. We present a formal description of the multirobot joint task allocation problem with heterogeneous capabilities and spatial constraints and an instantiation of the problem for the search and rescue domain. We introduce a novel declarative framework for modeling the problem as a mixed integer linear programming (MILP) problem and present a centralized anytime algorithm with error bounds. We demonstrate that our algorithm can outperform standard MILP solving techniques, greedy heuristics, and a market based approach which separates scheduling and task allocation. Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs. Abstract The periodic Lorentz gas is the dynamical system corresponding to the free motion of a point particle in a periodic system of fixed spherical obstacles of radius r centered at the integer points of the Euclidian plane, assuming all collisions of the particle with the obstacles to be elastic. In this Note, we study this motion on time intervals of order 1 r as r → 0 + . To cite this article: E. Caglioti, F. Golse, C. R. Acad. Sci. Paris, Ser. I 346 (2008). Constrained motion planning and Manipulation planning, for generic non-linear constraints, highly rely on the ability of solving non-linear equations. The Newton-Raphson method, often used in this context, is discontinuous with respect to its input and point wise path projection can lead to discontinuous constrained paths. The discontinuities come from the pseudo-inverse involved at each iteration of the Newton-Raphson algorithm. An interval of continuity for one iteration is derived from an upper bound of the norm of the Hessian of the constraints. Such a bound is easy to compute for constraints involving joint positions and orientations. We introduce two heuristical path projection algorithms and empirically show that they generate continuous constrained paths. The algorithms are integrated into a motion planning algorithm to empirically assert the continuity of the solution. This paper presents an algorithm that generates collision-free trajectories in three dimensions for multiple vehicles within seconds. The problem is cast as a non-convex optimization problem, which is iteratively solved using sequential convex programming that approximates non-convex constraints by using convex ones. The method generates trajectories that account for simple dynamics constraints and is thus independent of the vehicle's type. An extensive a posteriori vehicle-specific feasibility check is included in the algorithm. The algorithm is applied to a quadrocopter fleet. Experimental results are shown. In this paper, we introduce an algorithm for generating collision-free two-lane paths for unmanned vehicles used at mining sites by using quartic (degree 4) B-spline curves. Given the boundary geometry of the haul road area and the positions and orientations of the two-dimensional vehicle at the start and goal points, the algorithm automatically generates a collision-free two-lane path that satisfies the minimum turning radius constraint. Moreover, the resulting path shares the same third derivative at knots (joints), i.e., @math continuity, which guarantees a continuous rate of change of the curvature along the entire path. Examples are provided to demonstrate the effectiveness of the proposed algorithm.