Turning Radius Constraint Research Articles

Coverage Path Planning of UAV Based on Linear Programming—Fuzzy C-Means with Pigeon-Inspired Optimization

In contrast to rotorcraft, fixed-wing unmanned aerial vehicles (UAVs) encounter a unique challenge in path planning due to the necessity of accounting for the turning radius constraint. This research focuses on coverage path planning, aiming to determine optimal trajectories for fixed-wing UAVs to thoroughly explore designated areas of interest. To address this challenge, the Linear Programming—Fuzzy C-Means with Pigeon-Inspired Optimization algorithm (LP-FCMPIO) is proposed. Initially considering the turning radius constraint, a linear-programming-based model for fixed-wing UAV coverage path planning is established. Subsequently, to partition multiple areas effectively, an improved fuzzy clustering algorithm is introduced. Employing the pigeon-inspired optimization algorithm as the final step, an approximately optimal solution is sought. Simulation experiments demonstrate that the LP-FCMPIO, when compared to traditional FCM, achieves a more balanced clustering effect. Additionally, in contrast to traditional PIO, the planned flight paths display improved coverage of task areas, with an approximately 27.5% reduction in the number of large maneuvers. The experimental results provide validation for the effectiveness of the proposed algorithm.

On Hierarchical Multi-UAV Dubins Traveling Salesman Problem Paths in a Complex Obstacle Environment.

This article aims to solve a hierarchical multi-UAV Dubins traveling salesman problem (HMDTSP). Optimal hierarchical coverage and multi-UAV collaboration are achieved by the proposed approaches in a 3-D complex obstacle environment. A multi-UAV multilayer projection clustering (MMPC) algorithm is presented to reduce the cumulative distance from multilayer targets to corresponding cluster centers. A straight-line flight judgment (SFJ) was developed to reduce the calculation of obstacle avoidance. An improved adaptive window probabilistic roadmap (AWPRM) algorithm is addressed to plan obstacle-avoidance paths. The AWPRM improves the feasibility of finding the optimal sequence based on the proposed SFJ compared with a traditional probabilistic roadmap. To solve the solution to TSP with obstacles constraints, the proposed sequencing-bundling-bridging (SBB) framework combines the bundling ant colony system (BACS) and homotopic AWPRM. An obstacle-avoidance optimal curved path is constructed with a turning radius constraint based on the Dubins method and followed up by solving the TSP sequence. The results of simulation experiments indicated that the proposed strategies can provide a set of feasible solutions for HMDTSPs in a complex obstacle environment.

UAV 3D Trajectory Planning and Optimization Using A* Algorithm Based on Free Space Method

Due to the complexity of three-dimensional (3D) map modeling, the A* algorithm is inefficient in planning 3D trajectories for unmanned aerial vehicles (UAVs). This paper designs a method for planning 3D trajectories using A* algorithm based on free space method to address this issue. The method translates the 3D trajectory planning problem into a two-dimensional (2D) trajectory planning problem through flight surface extraction, thereby enhancing the efficiency of trajectory planning. In addition, a trajectory optimization method considering safety parameters and offset costs is designed for the waypoints that fail to meet UAV restrictions. The optimization method consists of longitudinal trajectory altitude adjustment and horizontal trajectory smoothing to ensure the trajectory aligns with the UAV climb rate constraint, normal overload constraint and minimum turning radius constraint. Simulation results show that the designed method delivers higher efficiency in 3D trajectory planning and optimization than the conventional method, and the optimized trajectory adheres to the above constraints.

Research on Automatic Vertical Parking Path-Planning Algorithms for Narrow Parking Spaces

Narrow parking spaces pose difficulties in path planning and spot turning caused by sudden changes and discontinuities in path curvature. To address these problems, this paper investigates the performance of three path-planning algorithms and proposes a path-optimization algorithm. First, a narrow parking space is defined based on single-step parking using the arc-line combination parking algorithm. Second, to compare the arc-line combination algorithm, Hybrid A* algorithm, and particle swarm optimization parking algorithm with respect to different narrow parking spaces, a multi-objective evaluation function is proposed, including three evaluation indicators, namely, the path length, the number of positive and negative conversions of vehicle speed, and the smoothness of the path. Their performance is compared using a simulation conducted in MATLAB. With the same starting point and different parking space widths, the three algorithms are simulated to generate different planned paths. Then, the evaluation indices are obtained to compare the performance of the algorithms based on the multi-objective function, the values of which indicate the fitness of the algorithm in a narrow parking environment. The results show that the Hybrid A* algorithm is better than the others for narrow parking spaces. Third, to smooth the planning path, a path optimization algorithm based on the cubic B-spline curve and gradient descent is proposed. Finally, the results of a simulation conducted on the proposed algorithm and the Hybrid A* algorithm are provided: the average minimum curvature of the path was reduced by 0.005 m−1, and the path meets the requirements of the minimum turning radius constraint of the analyzed vehicle. The results show that the proposed algorithm can effectively eliminate the curvature mutation point and constrain the path curvature to meet the requirements of a smooth path.

On Trajectory Homotopy to Explore and Penetrate Dynamically of Multi-UAV

This paper examines a trajectory homotopy optimization framework for multiple unmanned aerial vehicles (multi-UAV) to solve the problem of dynamic penetration mission planning (PMP) with hostile obstacles and perception constraints. Constrained problems are usually more challenging and difficult to solve with some practical constraints and requirements. To improve the efficiency of the solution for the penetration path, a novel variable-time mechanism has been constructed to adapt to the updated delay time of unknown target search (UTS) and dynamic trajectory planning (DTP) two stages. The occupancy grid maps are established by a Gaussian probability field (GPF) for predicting the positions of enemy UAVs. To fully consider the hostile obstacle constraint, a hybrid adaptive obstacle avoidance approach dynamic window PRM (DW-PRM) is designed to shorten the planned path. The penetration strategy algorithm (SG) is developed based on the proposed strategy set and decision tree. To improve the ability of dynamic obstacle avoidance, the multiple coupled penetration homotopy trajectory is addressed with a turning radius constraint. The simulation results indicated that the penetration homotopy framework for multi-constraints can solve the multi-UAV PMP problem.

Shortest Dubins Paths to Intercept a Target Moving on a Circle

We present a path planning problem for a pursuing unmanned aerial vehicle (UAV) to intercept a target traveling on a circle. The target is cooperative, and its position, heading, and speed are precisely known. The pursuing UAV has nonholonomic motion constraints, and therefore the path traveled must satisfy the minimum turn radius constraints. We consider the class of Dubins paths as candidate solutions, and analyze the characteristics of the six modes of Dubins paths where the final position is restricted to lie on the target circle with heading in the tangential direction of the circle. For each Dubins mode, we derive the feasibility limits, discontinuities, and local extrema. Using this analysis the intercepting paths are found by a systematic bisection search in the feasible regions of each of the Dubins modes. We prove that the algorithm finds the optimal (shortest length) intercepting path if it is a Dubins path. If the shortest intercepting path is not a Dubins path for any given instance, the algorithm finds a tight lower bound and an upper bound to the optimal solution.

Decentralized route-planning for multi-vehicle teams to satisfy a subclass of linear temporal logic specifications

Linear temporal logic (LTL) formulae are widely used to provide high level behavioral specifications on mobile robots. We propose a decentralized route-planning method for a networked team of mobile robots to satisfy a common (global) LTL specification. The global specification is assumed to be a conjunction of multiple formulae, each of which is treated as a task to be assigned to one or more vehicles. The vehicle kinematic model consists of two modes: a hover mode and a constant-speed forward motion mode with bounded steering rate. The proposed method leverages the consensus-based bundle algorithm for decentralized task assignment, thereby decomposing the global specification into local specifications for each vehicle. We develop a new algorithm to assign collaborative tasks: those simultaneously assigned to multiple vehicles. Rewards in the proposed task assignment algorithm are computed using the so-called lifted graph, which ensures the satisfaction of minimum turn radius constraints on vehicular motion. This algorithm synchronizes the vehicles’ routes with minimum waiting durations. The proposed method is compared against a multi-vehicle task assignment algorithm from the literature, which we extend to apply for satisfying LTL specifications. The proposed route-planning method is demonstrated via numerical simulation examples and a hardware implementation on networked single-board computers.

Event-Based Path-Planning and Path-Following in Unknown Environments for Underactuated Autonomous Underwater Vehicles

The paper addresses path planning and path-following problems in an unknown complex environment for an underactuated autonomous underwater vehicle (AUV). The AUV is required to follow a given reference path represented as a sequence of smoothly joined lines and arcs, bypassing obstacles encountered on the path. A two-level control system is proposed with an upper level for event-driven path planning and a lower level for path-following. A discrete event system is designed to identify situations that require planning a new path. An improved waypoint guidance algorithm and a Dubins curves based algorithm are proposed to build paths that allow the AUV to avoid collision with obstacles and to return to the reference path respectively. Both algorithms generate paths that meet the minimum turning radius constraint. A robust parameter-varying controller is designed using sublinear vector Lyapunov functions to solve the path-following problem. The performance of the developed event-based control system is demonstrated in three different simulation scenarios: with a sharp-edged obstacle, with a U-shaped obstacle, and with densely scattered obstacles. The proposed scheme does not require significant computing resources and allows for easy implementation on board.

Research on aircraft route planning optimization problem with multi-constraints and dual-targets

As the core technology in the field of aircraft, the route planning has attracted much attention. However, due to the complexity of the structure and performance constraints of the aircraft, the route planning algorithm does not have well universality, so it cannot be used in a complex environment. In the paper, a multi-constraints and dual-targets aircraft route planning model was established for the real-time requirements of space flight, the dynamic changes of flight environment with time, the accuracy requirements of positioning errors in the safety area, and the minimum turning radius constraints. Based on the directed graph and dynamic programming ideas, the model simulation and model validation were carried out with the data of F question in the “16th Graduate Mathematical Modeling Contest”. The results showed that the optimal path length obtained in data set 1 was 124.61 km, the number of corrections was 11 times, the solution time was 2.3768 seconds, the optimal path length obtained in data set 2 was 110.00 km, and the number of corrections was 12 times. The solution time was 0.0168 seconds. Multi-constraints and dual-targets aircraft route planning model can plan the flight path of the aircraft intuitively and timely, which confirmed the effectiveness of the model.

Integrated guidance and control framework for the waypoint navigation of a miniature aircraft with highly coupled longitudinal and lateral dynamics

A solution to the waypoint navigation problem for the fixed wing micro air vehicles (MAV) having a severe coupling between longitudinal and lateral dynamics, in the framework of integrated guidance and control (IGC) is addressed in this paper. IGC yields a single step solution to the waypoint navigation problem, unlike conventional multiple loop design. The pure proportional navigation (PPN) guidance law is integrated with the coupled MAV dynamics. A multivariable static output feedback (SOF) controller is designed for the linear state space model formulated in IGC framework. A waypoint navigation algorithm is proposed that handles the minimum turn radius constraint of the MAV and also evaluates the feasibility of reaching a waypoint. Non-linear simulations with and without wind disturbances are performed on a high fidelity 150 mm wingspan MAV model to demonstrate the proposed waypoint navigation algorithm.

Discrete vector fields for 2-D navigation under minimum turning radius constraints

To greatly extend the capabilities of unmanned aerial vehicles, automation systems for the various piloting functions are being developed. However, the development of these auto-systems is not without challenges. One of these challenges is the ability to prove the robustness of an autonomous system against unpredicted events. For the navigation task, this means to prove that the system can recover safely after a deviation from the original plan. In a decoupled scheme where the planner generates a plan online and the controller executes the plan, it is difficult to prove the safety of a system exhaustively. Conversely, using a feedback motion plan generated off-line, it is possible to pre-verify and pre-approve a large number of cases simultaneously. Therefore, it is easier to prove system safety. In this work, this approach is utilized to integrate the guidance toward a target location or a target path with geofence avoidance and recovery for a fully autonomous fixed-wing aircraft. Our formulation extends the wavefront expansion to the case of vehicles having minimum turning radius constraints. The solution is suitable for both single goal missions and path following problems in presence of geofences that can have both convex and non-convex shape. The main novelties introduced in the proposed method are the followings: (1) path following in presence of obstacles having an arbitrary shape, (2) definition of a transition function for the rotation of the flow around the predefined path, (3) use of a Gaussian filter to smooth the vector field. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Automatic Two-Lane Path Generation for Autonomous Vehicles Using Quartic B-Spline Curves

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., $C^3$ 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.

Fuzzy multiobjective cooperative surveillance of multiple UAVs based on distributed predictive control for unknown ground moving target in urban environment

In this paper, a fuzzy multiobjective path planning method based on distributed predictive control is proposed to deal with the problem of cooperative searching and tracking of unknown ground moving target by multiple unmanned aerial vehicles (UAVs) in urban environment. Firstly, extended Kalman filter (EKF) is combined with probability estimation to predict the states of the unknown target. Secondly, the line of sight occlusion of buildings, and energy consumptions of UAVs and sensors are considered in path planning. The objective functions are designed as target coverage degree, control input cost of UAV and sensor energy consumption respectively. The cooperative surveillance path planning problem is transformed into multiobjective optimization with different importance levels. Thirdly, distributed predictive control is used to obtain the local optimal path of each UAV. The predictive states of UAVs in finite horizon are exchanged to build the collision avoidance constraint, and the minimum turning radius constraint is also addressed. Then, all the objectives are fuzzified to handle the different importance level requirement. The sensor energy consumption function with switch value is equivalently converted using Sigmoid function and sign function. According to the principle that the objective with higher priority has higher satisfactory degree, preemptive priorities are transformed into the relaxed order of satisfactory degrees. The best path satisfying the requirement of multiobjective optimization and importance levels can be obtained. Finally, the simulation results show the effectiveness of the proposed method by comparing with traditional multiobjective weighted algorithm.

Multi-Target Motion Planning Amidst Obstacles for Autonomous Aerial and Ground Vehicles

The motion planning problem of a single autonomous vehicle having a minimum turn radius constraint, visiting an ordered sequence of targets in an environment with polygonal obstacles, is addressed. Two types of vehicles are considered: aerial/ground vehicle - described by the Dubins/Reeds-Shepp vehicle models, respectively. The problem is posed in the form of a search tree by using the obstacles’ vertices, vehicle’s initial configuration, and the set of target points as nodes. The tree’s arcs are represented by the Dubins/Reed-Shepp paths without terminal angle constraint (relaxed paths) connecting two adjacent nodes. These relaxed paths - connecting an initial configuration and a destination, are calculated using a feedback algorithm. Due to the computational complexity of the problem a genetic algorithm is proposed. Additionally, two deterministic search algorithms are presented. A quick heuristic greedy algorithm which uses the visibility graph distances for estimating the remaining vehicle path and an exhaustive algorithm which provides optimal solution trajectories. The performance of the algorithms is demonstrated and compared through sample runs and a Monte Carlo study. Results confirm that the heuristic algorithm provides relatively good solution for a small radius turn vehicle, while the genetic algorithm offers a good trade-off between computational load and performance.

Learning of skid-steered kinematic and dynamic models for motion planning

Modeling of the motion of a skid-steered robot is challenging since slippage and skidding is inherent to this type of platform and it requires high torques to perform curvilinear motion. If the ground–robot interaction and torque requirements are not captured properly, motion planners will sometimes generate trajectories that are not achievable by the robot. Important motion planning applications that rely heavily in these models, include energy efficient and momentum based planning. However, these models change as the terrain surface varies. To cope with this issue, this paper presents a methodology to perform online learning of such models. It combines detailed slip and terramechanic-based dynamic models of wheel–terrain interaction with online learning via Extended Kalman filtering (to update the kinematic model) and an efficient neural network formulation (to update the dynamic model). The proposed approach experimentally demonstrates the importance of the joint utilization of the learned vehicle models in the context of energy efficient motion planning. In particular, the slip-enhanced kinematic models are used to efficiently provide estimates of robot pose and the dynamic models are employed to generate energy estimates and minimum turn radius constraints.

Cooperative Multiple Pursuers against a Single Evader

This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified.

Dynamically feasible, energy efficient motion planning for skid-steered vehicles

Recent research has developed experimentally verified dynamic models for skid-steered wheeled vehicles and used these results to derive a power model for this important class of all-terrain vehicles. As presented in this paper, based on the torque limitations of the vehicle motors, the dynamic model can be used to develop payload and terrain-dependent minimum turn radius constraints and the power model can be used to predict the energy consumption of a given trajectory. This paper uses these results along with sampling based model predictive optimization to develop an effective methodology for generating dynamically feasible, energy efficient trajectories for skid-steered autonomous ground vehicles (AGVs) and compares the resultant trajectories with those based on the standard distance optimal trajectories. The simulated and experimental results consider an AGV moving at a constant forward velocity on both wood and asphalt surfaces under various payloads. The results show that a small increase in the distance of a trajectory over the distance optimal trajectory can result in a dramatic savings in the AGV's energy consumption. They also show that distance optimal planning can often produce trajectories that violate the motor torque constraints for skid-steered AGVs, which can result in poor navigation performance.

UAVs Task and Motion Planning in the Presence of Obstacles and Prioritized Targets.

The intertwined task assignment and motion planning problem of assigning a team of fixed-winged unmanned aerial vehicles to a set of prioritized targets in an environment with obstacles is addressed. It is assumed that the targets’ locations and initial priorities are determined using a network of unattended ground sensors used to detect potential threats at restricted zones. The targets are characterized by a time-varying level of importance, and timing constraints must be fulfilled before a vehicle is allowed to visit a specific target. It is assumed that the vehicles are carrying body-fixed sensors and, thus, are required to approach a designated target while flying straight and level. The fixed-winged aerial vehicles are modeled as Dubins vehicles, i.e., having a constant speed and a minimum turning radius constraint. The investigated integrated problem of task assignment and motion planning is posed in the form of a decision tree, and two search algorithms are proposed: an exhaustive algorithm that improves over run time and provides the minimum cost solution, encoded in the tree, and a greedy algorithm that provides a quick feasible solution. To satisfy the target’s visitation timing constraint, a path elongation motion planning algorithm amidst obstacles is provided. Using simulations, the performance of the algorithms is compared, evaluated and exemplified.

A Cooperative Pursuit-Evasion Game for Non-holonomic Systems

-This paper considers a pursuit-evasion game for non-holonomic systems where a number of pursuers attempt to capture a single evader in a bounded connected domain. The problem is challenging because all vehicles have the same manoeuvring capability and are subject to turn radius constraints making them non-holonomic systems. The paper initially presents simple and alternate proofs for results existing in the literature that guarantee capture for holonomic systems. These results that are based on the minimization of safe-reachable area (the set of points where an evader can travel without being caught) are then extended to non-holonomic systems. However, solving such a problem exactly is computationally intractable. Therefore, the paper proposes a computationally efficient algorithm to obtain an approximate solution to the safe-reachable area minimization problem where the pursuers aim to minimize the safe-reachable area of the evader, while the evader chooses control actions to maximize it. Also proposed is an alternative approach that uses a cooperative strategy based on a pure proportional navigation law to capture the evader. In the process, an evader strategy which is superior to those based on the minimization of safe-reachable area is identified. The paper evaluates the proposed algorithms through numerical simulations.

Coordinated Standoff Tracking Using Path Shaping for Multiple UAVs

A coordinated standoff target tracking strategy using path shaping for multiple unmanned aerial vehicles (UAVs) is presented. In performing a tracking mission of a ground target of interest, UAVs are to approach a target and to keep a standoff distance from it with a prescribed inter-vehicle angular separation around the target in order to track it while acquiring accurate target information. Since fixed-wing UAVs without hovering capability fly efficiently at a nominal airspeed, it is desirable that they can keep angular separation between vehicles while holding a constant velocity in a mission duration point of view. The work presented here introduces a new path shaping technique using two constant curvature segments satisfying the turn radius constraint and having more flexibility and fewer discontinuous points on a curvature command compared with the Dubins path at the expense of the path length. Moreover, a simultaneous arrival concept is introduced as a coordinated tracking strategy for multiple UAVs, which initialises UAVs on a standoff orbit with a desired angular separation. In order to address arrival time delay or failure of the UAV, a two-orbit approach is proposed in which UAVs first arrive at the outer orbit and subsequently shrink to the desired inner orbit at different times, while adjusting the angular separation between constant-speed UAVs. The feasibility and benefits of the proposed approach are evaluated via numerical simulations for a ground target using two cooperative UAVs.