Sequence Of Waypoints Research Articles

A numerically-stable trajectory generation and optimization algorithm for autonomous quadrotor UAVs

This paper introduces a novel trajectory generation and optimization algorithm (TGO) that enables agile and aggressive flight of quadrotor UAVs while considering various constraints associated with robot dynamics, actuator inputs, and flight environment. The TGO algorithm employs time-parametrized polynomial trajectories based on a predetermined sequence of waypoints to produce dynamically feasible and collision-free trajectories. This approach extends previous work that utilized differential flatness property and polynomial based trajectories by eliminating the need for iterative searching and computationally intensive sampling. One of the significant advantages of the TGO algorithm is its numerical stability for large number of waypoints and high-order polynomials. To address the ill-conditioned problem of Quadratic Programming (QP) based methods, the TGO algorithm reformulates the trajectory generation and optimization problem into an unconstrained quadratic programming (UCP) using the numerically stable null-space factorization method. The TGO algorithm produces minimum derivative trajectories and minimum waypoints arrival times, generating a wide range of aggressive trajectories that can leverage the full maneuvering capabilities of quadrotor robots. The proposed algorithm’s numerical stability and computational advantages are demonstrated through various scenarios and comparisons. An animated simulation of the TGO algorithm is available at: https://youtu.be/MvvhBG14iIg.

Data harvesting in uncharted waters: Interactive learning empowered path planning for USV-assisted maritime data collection under fully unknown environments

Unleashing the potential of unmanned surface vehicles (USVs) for Underwater Internet-of-Things (UIoT) brings forth a vigorous new frontier, unlocking the innovative insights and paving the way towards the era of Smart Ocean. By leveraging the power of USVs, this paper dives into the path planning problem in oceanic data collection, particularly in fully unknown environments. First, by encapsulating the intricacies of USV-sensor communication channel and obstacle avoidance mechanism, a novel path planning model for data collection is meticulously formulated, providing a comprehensive and in-depth portrayal of the underlying dynamics. Secondly, integrating an environmental updating mechanism, an interactive learning approach is intentionally developed to enable USVs to fully exploit and explore the dynamic environments, employing a heuristically defined reward function to generate optimal waypoint sequence for USVs. Catering to the non-holonomic nature of USVs, the fast-discrete Clothoid path is introduced to formulate the USVs’ trajectories, whereby smooth maneuvering is achieved by governing feasible actions under kinematic constraints, maintaining the continuous alteration of curvature and course at turning points. The convergence capability of the method is proved both theoretically and demonstrated numerically. Extensive simulation and comparative evaluations under complex oceanic environments showcase its strong practical applicability, thereby demonstrating the promising potential of this approach in unlocking new opportunities for innovation and exploration in UIoT.

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Planning an achievable trajectory for a mobile robot usually consists of two steps: (i) finding a path in the form of a sequence of discrete waypoints and (ii) transforming this sequence into a continuous and smooth curve. To solve the second problem, this paper proposes algorithms for automatic dynamic smoothing of the primary path using a tracking differentiator with sigmoid corrective actions. Algorithms for setting the gains of the differentiator are developed, considering a set of design constraints on velocity, acceleration, and jerk for various mobile robots. When tracking a non-smooth primary path, the output variables of the differentiator generate smooth trajectories implemented by a mechanical plant. It is shown that the tracking differentiator with a different number of blocks also generates derivatives of the smoothed trajectory of any required order, taking into account the given constraints. Unlike standard analytical methods of polynomial smoothing, the proposed algorithm has a low computational load. It is easily implemented in real time on the on-board computer. In addition, simple methods for modeling a safety corridor are proposed, taking into account the dimensions of the vehicle when planning a polygon with stationary obstacles. Confirming results of numerical simulation of the developed algorithms are presented.

Optimal Path Planning Through a Sequence of Waypoints

This letter presents a deterministic approach for finding the optimal path through a sequence of spatial waypoints while accounting for vertex or turn costs. A case study is presented where the proposed algorithm is used to determine the optimal path through a sequence of waypoints. This is then compared with the path obtained when considering only two consecutive waypoints at a time. Further, an approximation that uses three waypoints at a time in a staggered manner is described. This approach is shown to be computationally efficient and finds the optimal path even in cases with 2000 waypoints.

Time‐sensitive coverage control for non‐holonomic and heterogeneous robots: An extremum seeking framework and application

AbstractThis work addresses a time‐sensitive coverage control problem for multiple non‐holonomic mobile robots. The coverage objective is evaluated by the total arrivial time of robots reaching their dominant clients with the predefined constant but heterogeneous velocities. An extremum‐seeking control framework is proposed, including a numerical optimizer that iteratively produces the optimal waypoints of robots minimizing the total arriving time and a state regulator that drives the robot's positions to the optimal locations under both constraints non‐holonomic kinematic model and the constant‐velocity. An improved K‐means algorithm is first designed to produce the waypoint sequence. A theoretical analysis of the convergence of coverage objectives is provided. Then a fixed‐time state regulator for the robot's angular velocity is derived from regulating robot positions to the desired waypoints within each time step that varies with the heterogeneous traversing velocity and the distance between waypoints. Finally, the results are validated by a virtual robotic simulation platform and the experiment on real robots, showing that the proposed methods can efficiently deploy multiple heterogeneous robots for time‐sensitive services to clients with a discrete distribution. The simulation and experimental code are open‐sourced at https://gitee.com/ahu‐icip/simulation.git.

A Convex Programming Approach to Multipoint Optimal Motion Planning for Unicycle Robots

An important extension of point-to-point motion planning deals with navigating a robot optimally through a sequence of waypoints. The resulting multipoint problem is typically nonconvex due to the requirement to optimize the waypoint passage time, which has hindered the determination of globally optimal solutions. In this paper, a new motion planning technique is presented for multipoint problems involving unicycle robots. Our main finding is that, by adopting a cost function that weights a combination of path length and maneuver time, together with a suitable tightening of the control input constraints, such type of problems can be cast as a convex program. This can be solved in polynomial time to obtain a global optimum. The proposed motion planner is compared to time-optimal trajectory generation scheme based on nonlinear programming, and it can find better trajectories than this method while being computationally faster.

Dynamic and Nonlinear Programming for Trajectory Planning

Direct optimal control techniques, relying on numerical methods for constrained optimization, are typically used in trajectory planning tasks in high-dimensional spaces. However, general-purpose solvers often fail to find a feasible solution when facing cluttered environments. Sampling-or graph-based methods, instead, can explore complex configuration spaces but struggle with dynamic constraints. Here, we propose to combine dynamic programming (DP) and derivative-based methods to reliably solve trajectory planning problems. Specifically, we exploit DP to generate a sequence of waypoints in a lowdimensional space, which are then encoded as pointwise path constraints for a high-dimensional trajectory, whose constraint violations are then represented as a penalty within the Bellman equation to recompute the waypoints. This iterative approach, alternating path and trajectory optimization, avoids both the curse of dimensionality for DP and problematic nonconvexities (such as obstacles) for motion planning. We demonstrate our strategy using numerical experiments on a six-degree-of-freedom robotic manipulator moving in a confined space.

Learning Minimum-Time Flight in Cluttered Environments

We tackle the problem of minimum-time flight for a quadrotor through a sequence of waypoints in the presence of obstacles while exploiting the full quadrotor dynamics. Early works relied on simplified dynamics or polynomial trajectory representations that did not exploit the full actuator potential of the quadrotor, and, thus, resulted in suboptimal solutions. Recent works can plan minimum-time trajectories; yet, the trajectories are executed with control methods that do not account for obstacles. Thus, a successful execution of such trajectories is prone to errors due to model mismatch and in-flight disturbances. To this end, we leverage deep reinforcement learning and classical topological path planning to train robust neural-network controllers for minimum-time quadrotor flight in cluttered environments. The resulting neural network controller demonstrates substantially better performance of up to 19% over state-of-the-art methods. More importantly, the learned policy solves the planning and control problem simultaneously online to account for disturbances, thus achieving much higher robustness. As such, the presented method achieves 100% success rate of flying minimum-time policies without collision, while traditional planning and control approaches achieve only 40%. The proposed method is validated in both simulation and the real world, with quadrotor speeds of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$42 \,\mathrm{k}\mathrm{m}\mathrm{h}^{-1}$</tex-math></inline-formula> and accelerations of 3.6 g.

Time-Optimization of Trajectories Using Zero-Clamped Cubic Splines and Their Analytical Gradients

Modern flexible production systems benefit from collaborative robot systems that support to teach robot configurations by hand to quickly implement collision-free motions. However, appropriate interpolation schemes that allow a fast and smooth motion through this sequence of waypoints is often not part of robot control systems. Instead, only point-to-point motions or a set of predefined curves like circular motions are supported. We propose an approach to improve the efficiency of finding a time parameterization with cubic splines that computes minimum trajectory durations while respecting actuator limits and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C^2$</tex-math></inline-formula> -continuity. Compared to the existing method, our contribution consists in the analytical gradients of the underlying nonlinear optimization problem and thus we are able to propose an efficient solution approach using state-of-the-art optimization solvers. We validate our implementation in simulation and in experiments, and benchmark it with the three trajectory generation methods implemented in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MoveIt!</i> .

A node selection algorithm to graph-based multi-waypoint optimization navigation and mapping

Autonomous robot multi-waypoint navigation and mapping have been demanded in many real-world applications found in search and rescue (SAR), environmental exploration, and disaster response. Many solutions to this issue have been discovered via graph-based methods in need of switching the robotos trajectory between the nodes and edges within the graph to create a trajectory for waypoint-to-waypoint navigation. However, studies of how waypoints are locally bridged to nodes or edges on the graphs have not been adequately undertaken. In this paper, an adjacent node selection (ANS) algorithm is developed to implement such a protocol to build up regional path from waypoints to nearest nodes or edges on the graph. We propose this node selection algorithm along with the generalized Voronoi diagram (GVD) and Improved Particle Swarm Optimization (IPSO) algorithm as well as a local navigator to solve the safety-aware concurrent graph-based multi-waypoint navigation and mapping problem. Firstly, GVD is used to form a Voronoi diagram in an obstacle populated environment to construct safety-aware routes. Secondly, the sequence of multiple waypoints is created by the IPSO algorithm to minimize the total travelling cost. Thirdly, while the robot attempts to visit multiple waypoints, it traverses along the edges of the GVD to plan a collision-free trajectory. The regional path from waypoints to the nearest nodes or edges needs to be created to join the trajectory by the proposed ANS algorithm. Finally, a sensor-based histogram local reactive navigator is adopted for moving obstacle avoidance while local maps are constructed as the robot moves. An improved -spline curve-based smooth scheme is adopted that further refines the trajectory and enables the robot to be navigated smoothly. Simulation and comparison studies validate the effectiveness and robustness of the proposed model.

Method of an unmanned aerial vehicle composition route in space

The article is devoted to the development of a method of composition of the route of an unmanned aerial vehicle in three-dimensional space. The main difference of the presented method is the complex consideration of the features of the environment, which reflects the possible obstacles (active or passive) and other limitations of the problem when composing the route of the unmanned aerial vehicle in three-dimensional space. This allowed to increase the safety of the task in autonomous flight conditions. The article analyzes the main approaches to the composition of unmanned aerial vehicle routes in space. The conclusion about the shortcomings of the two-dimensional representation is made. The method presents four stages of the task. This is the stage of modeling the environment that reflects possible obstacles (active or passive) and other limitations of the task. Stage of construction of an extended graph of unmanned aerial vehicle routes in space. The difference of this stage is the adaptive consideration of the spatial location of active obstacles in space. The next stage is the route search stage, which connects the starting point with the end and bypasses all obstacles and allows you to build a starting route in the form of a broken line, which is formed by a sequence of waypoints, and connects the starting point with the end, bypassing obstacles. The last is the stage of obtaining the final result, which is provided by smoothing the obtained broken line. In this part of the composition method, to solve the problem of smoothing the trajectory of the unmanned aerial vehicle in space on the selected route, the expediency of using the method of non-uniform cubic B-spline is proved. With the help of this method the task of selection and optimization of the smoothing parameter is set and solved.

Conditionally Markov Modeling and Optimal Estimation for Trajectory With Waypoints and Destination

On a grand scale, motion trajectories are usually defined by an origin, a sequence of waypoints, and a destination. A typical example is in air traffic management (ATM), where a flight from an origin passes several waypoints and arrives at a destination. The origin, the waypoints, and the destination contain useful information for trajectory modeling. On the other hand, due to trajectory design criteria and ATM restrictions and requirements, there are long-range dependencies in a flight trajectory. Such dependencies can be modeled by taking the origin, waypoints, and destination into account in trajectory modeling. In this article, we propose a class of conditionally Markov (CM) sequences to model such trajectories with long-range dependencies. First, we define a general CM sequence as a foundation. Then, we discuss its special cases for different scenarios. We derive dynamic models of these CM sequences in the Gaussian case. We show how parameters of the models can be learned from data or designed. We also justify the use of the proposed CM models for trajectory modeling. In addition, we obtain optimal filters and predictors for different models. Simulation demonstrations are given.

Path Planning Followed by Kinodynamic Smoothing for Multirotor Aerial Vehicles (MAVs)

Any obstacle-free path planning algorithm, in general, gives a sequence of waypoints that connect start and goal positions by a sequence of straight lines, which does not ensure the smoothness and the dynamic feasibility to maneuver the MAV. Kinodynamic-based motion planning is one of the ways to impose dynamic feasibility in planning. However, kinodynamic motion planning is not an optimal solution due to high computational demands for real-time applications. Thus, we explore path planning followed by kinodynamic smoothing while ensuring the dynamic feasibility of MAV. The main difference in the proposed technique is not to use kinodynamic planning when finding a feasible path, but rather to apply kinodynamic smoothing along the obtained feasible path. We have chosen a geometric-based path planning algorithm “RRT*” as the path finding algorithm. In the proposed technique, we modified the original RRT* introducing an adaptive search space and a steering function that helps to increase the consistency of the planner. Moreover, we propose a multiple RRT* that generates a set of desired paths. The optimal path from the generated paths is selected based on a cost function. Afterwards, we apply kinodynamic smoothing that will result in a dynamically feasible as well as obstacle-free path. Thereafter, a b-spline-based trajectory is generated to maneuver the vehicle autonomously in unknown environments. Finally, we have tested the proposed technique in various simulated environments. According to the experiment results, we were able to speed up the path planning task by 1.3 times when using the proposed multiple RRT* over the original RRT*.

An Open-Source Testbed for Outdoor Navigation With the AR.Drone Quadrotor

The development and the experimental validation of a workbench capable of supporting outdoor flights using basically the affordable commercial quadrotor AR.Drone 2.0 and a personal computer is considered in this article. The text discusses some technical details of the developed system, focusing on how to achieve real-time navigation adopting a simplified dynamic model as a high-level representation of the vehicle in flight, a general-purpose nonlinear controller, suitable for different types of control applications, and a sensor fusion algorithm, designed to compensate for delayed measurements in the available sensory data. To check the effectiveness of such testbed, results associated to some experimental flights are presented, with the vehicle accomplishing positioning tasks, considering a fixed target point and a sequence of waypoints, and trajectory tracking tasks. Such results, associated to the theoretical analysis provided, allow claiming that the proposed system is an efficient way to guide the vehicle to accomplish different tasks. Additionally, the source code used is available for free download and modification, resulting in a valuable open-source workbench for researchers just starting working with aerial robotics.

A Waypoint Tracking Controller for Autonomous Road Vehicles Using ROS Framework.

Automated Driving Systems (ADSs) require robust and scalable control systems in order to achieve a safe, efficient and comfortable driving experience. Most global planners for autonomous vehicles provide as output a sequence of waypoints to be followed. This paper proposes a modular and scalable waypoint tracking controller for Robot Operating System (ROS)-based autonomous guided vehicles. The proposed controller performs a smooth interpolation of the waypoints and uses optimal control techniques to ensure robust trajectory tracking even at high speeds in urban environments (up to 50 km/h). The delays in the localization system and actuators are compensated in the control loop to stabilize the system. Forward velocity is adapted to path characteristics using a velocity profiler. The controller has been implemented as an ROS package providing scalability and exportability to the system in order to be used with a wide variety of simulators and real vehicles. We show the results of this controller using the novel and hyper realistic CARLA Simulator and carrying out a comparison with other standard and state-of-art trajectory tracking controllers.

Swarm and Multi-agent Time-based A* Path Planning for Lighter-Than-Air Systems

This work develops and implements a multi-agent time-based path-planning method using A*. The purpose of this work is to create methods in which multi-agent systems can coordinate actions and complete them at the same time. We utilized A* with constraints defined by a dynamic model of each agent. The model for each agent is updated during each time step and the resulting control is determined. This results in a translational path that each of the agents is physically capable of completing in synchrony. The resulting path is given to the agents as a sequence of waypoints. Periodic updates of the path are calculated, utilizing real-world position and velocity information, as the agents complete the task to account for external disturbances. Our methodology is tested in a dynamic simulation environment as well as on real-world lighter-than-air robotic agents.

System Level Modeling and Control Design of hTetrakis–A Polyiamond Inspired Self-Reconfigurable Floor Tiling Robot

Fixed morphology cleaning robots mostly face significant challenges in cleaning the narrow spaces in the environment. To overcome this, a new class of self-reconfigurable floor cleaning robot, hTetrakis, made of four triangular blocks, is built. This paper focuses on the modeling and controller design of the locomotion and reconfiguration mechanism of the platform. The locomotion of the platform with respect to the velocity of the wheels is formulated based on the kinematic analysis. By modeling the system in Simscape multibody toolbox of Matlab, the maneuverability of the platform is studied. The reconfiguration of the platform is studied based on the dynamics of individual block about the hinged joint. The control architecture of this platform has two distinct Proportional-Integral-Derivative (PID) controllers to eliminate the position error during reconfiguration, and to maintain the platform’s velocity. The coverage path planning of the platform is based on the classical Travelling Salesman Problem which finds the optimal sequence of waypoints as per the minimal energy consumption. Real time experiments are carried out to validate the effectiveness of the proposed control schemes in terms of eliminating the velocity errors, and maintaining the desired trajectory.

An Improved Fuzzy Logic Control Method for Path Tracking of an Autonomous Vehicle

Highlights This study focused on the path tracking accuracy of a two-wheel steering, two-wheel drive autonomous vehicle. An improved fuzzy logic control method (IFM) was designed to control the steering angle of the front wheels. The IFM was better than traditional pure pursuit and fuzzy logic control methods for automatic path tracking. Abstract. This article presents a path-tracking algorithm based on an improved fuzzy logic control method (IFM) that generates optimal steering angles for an autonomous wheeled vehicle to track a sequence of waypoints. The path-tracking algorithm was designed to focus on the vehicle performance, including tracking accuracy, stability, and convergence speed. A prototype vehicle with two-wheel steering and two-wheel drive (2WS-2WD) was developed as a test platform and equipped with a series of sensors for evaluating the IFM. In this study, we considered two variables, i.e., lateral deviation (d) and heading deviation (θ), as inputs for the control system. The output (δ) was the steering angle of the front wheels as controlled by an electric linear actuator. A maximum steering angle strategy was adopted for rapid convergence when the vehicle was far from the desired path or when the heading deviation was large. An update-line distance algorithm was used for finding the best turning time as the vehicle moved closer to the next waypoint. To validate the proposed algorithm, testing was performed to compare traditional pure pursuit (TPP), traditional fuzzy logic control method (TFM), and the IFM in tracking two types of paths (straight and rectangular). Traveling at 0.5 m s-1 and with a signal sampling period of 0.5 s, the prototype converged to the desired straight path from different initial states. When the vehicle reached a stable state, the steady-state error was between 5.0 and 6.5 cm with a mean of ≤6.0 cm. The settling distance in the straight path test was between 125.0 and 422.3 cm, and the convergence time was in the range of 11.5 to 16.0 s; the greater the initial deviation of the vehicle was, the greater the settling distance and settling time were. In the 15 m x 14 m rectangular path test, the overall mean error of the IFM was 14.4 cm when the initial lateral and heading deviations were 0, and the maximum deviation was 67.4 cm, which occurred at the corners. The test results show that the proposed IFM had better accuracy, stability, and convergence speed for path tracking when compared to the TPP and TFM algorithms.

Lagrange modeling and navigation based on quaternion for controlling a micro AUV under perturbations

This paper addresses the modeling of an autonomous underwater vehicle using quaternion formulation for angular position description and Lagrange method to compute the equations of motion. As the four parameters are dependent and generate a constraint, Lagrange multipliers are used with Baumgarte method to solve and stabilize the system. The dynamic model includes underwater effects like added mass and inertia, hydrodynamic damping, buoyancy and propeller forces. Moreover, a quaternion-based line of sight guidance algorithm is derived to avoid any use of trigonometric function and compute directly the orientation error of the underwater vehicle and the desired attitude in terms of quaternions. Motion control is achieved with a quaternion-based adaptive sliding mode controller rejecting model uncertainties and water current. The simulation results, where the vehicle follows a sequence of way-points including vertical diving motion demonstrate that the proposed guidance algorithm and motion control are deeply relevant both in terms of effectiveness and robustness for this particular type of vehicle and orientation formulation.

A Boundary Node Method for path planning of mobile robots

In this paper we propose a new method for solving the path planning problem in a static environment to find an optimal collision-free path between starting and goal points. First, the grid model of the robot’s working environment is constructed, and then the potential value of the grid cells is calculated based on the new proposed potential function. This function is used to guide the robot to move toward the desired goal, it has the lowest value at the goal position and the value is increased as the robot moves further away. Second, we developed an efficient method, called the Boundary Node Method, to find the initial feasible path. In this method, the robot is simulated by a nine-node quadrilateral element, where the centroid node represents the robot’s position. The robot moves in the working environment toward the goal with eight-boundary nodes based on the potential value of the boundary nodes. The initial feasible path is generated from a sequence of waypoints that the robot has to traverse as it moves toward the goal point without colliding with any obstacles. However, the proposed method can generate the path safely and efficiently, but the path is not optimal in terms of the total path length. Therefore, in order to construct an optimal or near-optimal collision-free path, an additional method, called the Path Enhancement Method, is developed. Finally, the cubic spline interpolation is adopted to generate a continuous smooth path that connects the starting point to the goal point. The proposed method has been tested in several working environments with different degrees of complexities. The results demonstrated that the proposed method is able to generate near-optimal collision-free path efficiently. Moreover, we compared the performance of the proposed methods with the other path planning methods in terms of path length and computational time. The results revealed that the proposed method can solve the robot path planning problem more efficiently. Finally, in order to verify the performance of the developed method for generating a collision-free path, experimental studies were carried out on the real robot.