Real-time Trajectory Planning Research Articles

Suboptimal Trajectory Planning Technique in Real UAV Scenarios with Partial Knowledge of the Environment

In recent years, the issue of trajectory planning for autonomous unmanned aerial vehicles (UAVs) has received significant attention due to the rising demand for these vehicles across various applications. Despite advancements, real-time trajectory planning remains computationally demanding, particularly with the inclusion of 3D localization using computer vision or advanced sensors. Consequently, much of the existing research focuses on semi-autonomous systems, which rely on ground assistance through the use of external sensors (motion capture systems) and remote computing power. This study addresses the challenge by proposing a fully autonomous trajectory planning solution. By introducing a real-time path planning algorithm based on the minimization of the snap, the optimal trajectory is dynamically recalculated as needed. Evaluation of the algorithm’s performance is conducted in an unknown real-world scenario, utilizing both simulations and experimental data. The algorithm was implemented in MATLAB and subsequently translated to C++ for onboard execution on the drone.

Real-time Trajectory Planning and Tracking Control of Bionic Underwater Robot in Dynamic Environment.

In this article, we study the trajectory planning and tracking control of a bionic underwater robot under multiple dynamic obstacles. We first introduce the design of the bionic leopard cabinet underwater robot developed in our lab. Then, we model the trajectory planning problem of the bionic underwater robot by combining its dynamics and physical constraints. Furthermore, we conduct global trajectory planning for bionic underwater robots based on the temporal-spatial Bezier curves. In addition, based on the improved proximal policy optimization, local dynamic obstacle avoidance trajectory replanning is carried out. In addition, we design the fuzzy proportional-integral-derivative controller for tracking control of the planned trajectory. Finally, the effectiveness of the real-time trajectory planning and tracking control method is verified by comparative simulation in dynamic environment and semiphysical simulation of UWSim. Among them, the real-time trajectory planning method has advantages in trajectory length, trajectory smoothness, and planning time. The error of trajectory tracking control method is controlled around 0.2 m.

Real-Time Trajectory Planning and Obstacle Avoidance for Human–Robot Co-Transporting

Real-Time Trajectory Planning and Obstacle Avoidance for Human–Robot Co-Transporting

Hardware–Software Embedded System for Real-Time Trajectory Planning of Multi-Axis Machine Using B-Spline Curve Interpolation Algorithm

Hardware–Software Embedded System for Real-Time Trajectory Planning of Multi-Axis Machine Using B-Spline Curve Interpolation Algorithm

Deep Learning-Based Trajectory Planning and Control for Autonomous Ground Vehicle Parking Maneuver

In this paper, a novel integrated real-time trajectory planning and tracking control framework capable of dealing with autonomous ground vehicle (AGV) parking maneuver problems is presented. In the motion planning component, a newly-proposed idea of utilizing deep neural networks (DNNs) for approximating optimal parking trajectories is further extended by taking advantages of a recurrent network structure. The main aim is to fully exploit the inherent relationships between different vehicle states in the training process. Furthermore, two transfer learning strategies are applied such that the developed motion planner can be adapted to suit various AGVs. In order to follow the planned maneuver trajectory, an adaptive learning tracking control algorithm is designed and served as the motion controller. By adapting the network parameters, the stability of the proposed control scheme, along with the convergence of tracking errors, can be theoretically guaranteed. In order to validate the effectiveness and emphasize key features of our proposal, a number of experimental studies and comparative analysis were executed. The obtained results reveal that the proposed strategy can enable the AGV to fulfill the parking mission with enhanced motion planning and control performance. <i>Note to Practitioners</i>&#x2014;This article was motivated by the problem of optimal automatic parking planning and tracking control for autonomous ground vehicles (AGVs) maneuvering in a restricted environment (e.g., constrained parking regions). A number of challenges may arise when dealing with this problem (e.g., the model uncertainties involved in the vehicle dynamics, system variable limits, and the presence of external disturbances). Existing approaches to address such a problem usually exploit the merit of optimization-based planning/control techniques such as model predictive control and dynamic programming in order for an optimal solution. However, two practical issues may require further considerations: 1). The nonlinear (re)optimization process tends to consume a large amount of computing power and it might not be affordable in real-time; 2). Existing motion planning and control algorithms might not be easily adapted to suit various types of AGVs. To overcome the aforementioned issues, we present an idea of utilizing the recurrent deep neural network (RDNN) for planning optimal parking maneuver trajectories and an adaptive learning NN-based (ALNN) control scheme for robust trajectory tracking. In addition, by introducing two transfer learning strategies, the proposed RDNN motion planner can be adapted to suit different AGVs. In our follow-up research, we will explore the possibility of extending the developed methodology for large-scale AGV parking systems collaboratively operating in a more complex cluttered environment.

Real-Time Trajectory Planning for Hypersonic Entry Using Adaptive Non-Uniform Discretization and Convex Optimization

This paper introduces an improved sequential convex programming algorithm using adaptive non-uniform discretization for the hypersonic entry problem. In order to ensure real-time performance, an inverse-free precise discretization based on first-order hold discretization is adopted to obtain a high-accuracy solution with fewer temporal nodes, which would lead to constraint violation between the temporal nodes due to the sparse time grid. To deal with this limitation, an adaptive non-uniform discretization is developed, which provides a search direction for purposeful clustering of discrete points by adding penalty terms in the problem construction process. Numerical results show that the proposed method has fast convergence with high accuracy while all the path constraints are satisfied over the time horizon, thus giving potential to real-time trajectory planning.

Trajectory Planning for Mobile Manipulators with Control Constraints

This paper presents the method of trajectory planning for mobile manipulators considering limitations resulting from capabilities of robotic system actuators. The fulfillment of control constraints is achieved by introducing virtual control scaling of the robot trajectory in the limited periods of time. Such an approach allows researchers to obtain the trajectories fulfilling control constraints without significantly increasing the time of task execution. The proposed method generates sub-optimal trajectories maximizing the manipulability measure of the robot arm, preserves mechanical and collision avoidance limitations and can be used in real-time trajectory planning. The effectiveness of the presented solution is confirmed by computer simulations involving a mobile manipulator with parameters corresponding to KUKA youBot.

Speed-First: An Aggressive Gradient-Based Local Planner for Quadrotor Faster Flight

Autonomous flight for quadrotors is maturing with the development of real-time local trajectory planning. However, the current local planning method is too conservative to waste the agility of the quadrotors. So in this paper, we have focused on aggressive local trajectory planning and proposed a gradient-based planning method to rapidly plan faster executable trajectories while ensuring it is collision-free. A distance gradient information generation strategy is proposed, which finds a collision-free Hybrid-A* path to replace the control points in obstacles for safety and creates the distance gradient used in the back-end optimization. Besides, we present a novel and aggressive time span cost term to tackle unfeasibility and improve the overall trajectory speed. Extensive simulations and real-world experiments are tested to validate our method. The results show that our proposed method generates a more aggressive trajectory with a shorter planning time and a faster flight speed than the classical gradient-based method.

Real-time online trajectory planning and guidance for terminal area energy management of unmanned aerial vehicle

&lt;p style='text-indent:20px;'&gt;Aiming at the energy management problem of unmanned aerial vehicles (UAVs) in the terminal area energy management (TAEM) phase, a real-time online trajectory planning and guidance strategy based on judging energy is proposed. The trajectory planning strategy estimates the flight profile online in real time by judging the energy and changing the radius of the heading alignment circle. In addition, guidance instructions are also obtained at once. In the S-turn stage, the lateral guidance adopts a closed loop control mode with a fixed bank angle. In the remaining stage, the lateral guidance adopts a closed loop control mode for tracking the azimuth angle. In all stages, the longitudinal guidance adopts a closed loop control mode for tracking the flight path angle and flight height. The trajectory planning strategy is able to quickly generate a reference trajectory for testing cases with large variations not only in the initial energy but also in the energy of the flight process. The simulation results show that the proposed trajectory planning and guidance strategy can effectively manage a UAV's energy in the TAEM phase, ensuring that the UAV lands safely.&lt;/p&gt;

Gaze-based Shared Autonomy Framework with Real-time Action Primitive Recognition for Robot Manipulators.

Robots capable of robust, real-time recognition of human intent during manipulation tasks could be used to enhance human-robot collaboration for activities of daily living. Eye gaze-based control interfaces offer a non-invasive way to infer intent and reduce the cognitive burden on operators of complex robots. Eye gaze is traditionally used for "gaze triggering" (GT) in which staring at an object, or sequence of objects, triggers pre-programmed robotic movements. We propose an alternative approach: a neural network-based "action prediction" (AP) mode that extracts gaze-related features to recognize, and often predict, an operator's intended action primitives. We integrated the AP mode into a shared autonomy framework capable of 3D gaze reconstruction, real-time intent inference, object localization, obstacle avoidance, and dynamic trajectory planning. Using this framework, we conducted a user study to directly compare the performance of the GT and AP modes using traditional subjective performance metrics, such as Likert scales, as well as novel objective performance metrics, such as the delay of recognition. Statistical analyses suggested that the AP mode resulted in more seamless robotic movement than the state-of-the-art GT mode, and that participants generally preferred the AP mode.

DQN-Based Proactive Trajectory Planning of UAVs in Multi-Access Edge Computing

The main aim of future mobile networks is to provide secure, reliable, intelligent, and seamless connectivity. It also enables mobile network operators to ensure their customer’s a better quality of service (QoS). Nowadays, Unmanned Aerial Vehicles (UAVs) are a significant part of the mobile network due to their continuously growing use in various applications. For better coverage, cost-effective, and seamless service connectivity and provisioning, UAVs have emerged as the best choice for telco operators. UAVs can be used as flying base stations, edge servers, and relay nodes in mobile networks. On the other side, Multi-access Edge Computing (MEC) technology also emerged in the 5G network to provide a better quality of experience (QoE) to users with different QoS requirements. However, UAVs in a mobile network for coverage enhancement and better QoS face several challenges such as trajectory designing, path planning, optimization, QoS assurance, mobility management, etc. The efficient and proactive path planning and optimization in a highly dynamic environment containing buildings and obstacles are challenging. So, an automated Artificial Intelligence (AI) enabled QoS-aware solution is needed for trajectory planning and optimization. Therefore, this work introduces a well-designed AI and MEC-enabled architecture for a UAVs-assisted future network. It has an efficient Deep Reinforcement Learning (DRL) algorithm for real-time and proactive trajectory planning and optimization. It also fulfills QoS-aware service provisioning. A greedy-policy approach is used to maximize the long-term reward for serving more users with QoS. Simulation results reveal the superiority of the proposed DRL mechanism for energy-efficient and QoS-aware trajectory planning over the existing models.

Hybrid deterministic non-deterministic data-parallel algorithm for real-time unmanned aerial vehicle trajectory planning in CUDA

The development of autonomous Unmanned Aerial Vehicles (UAVs) is a priority to many civilian and military organizations. Real time optimal trajectory planning is an essential element for the autonomy of UAVs. The use of metaheuristic algorithms for solving such complex optimization problems with non-linearity and multimodality has gained popularity recently. In this paper, we use a non-deterministic Flower Pollination Algorithm (FPA) to deal with the problem's complexity and compute feasible and quasi-optimal trajectories for fixed-wing UAVs in complex 3D environments, taking into account the vehicle's flight properties. The global optimization algorithm is improved with the addition of a deterministic 2-opt local search providing a significant improvement. To achieve real-time performance, the proposed trajectory planner in implemented and parallelized following the data-parallel paradigm on a Graphics Processing Unit (GPU) using the Compute Unified Device Architecture (CUDA) resulting in a 253.4x speedup compared to the sequential implementation on CPU. The parallel implementation is able to compute quasi-optimal trajectories in just 0.369 s.

A Time-Optimal Trajectory Planning Strategy for an Aircraft With a Suspended Payload via Optimization and Learning Approaches

In this article, a real-time interactive time-optimal trajectory planning (TOTP) strategy is proposed for aircraft slung-load systems, in which the practical performance is guaranteed by taking advantage of convex optimization and reinforcement learning (RL) techniques. To the best of our knowledge, it is the first TOTP solution for an aircraft suspension system subject to path, velocity, acceleration, and cable tension constraints, where a practice-oriented RL policy is designed to interact with the system online. Specifically, by exploring the differential flatness property of the system, the states are projected into path coordinate space, where all the physical constraints are formulated in the TOTP with convex forms. Then, the TOTP is transformed into a large sparse optimization problem after discretization, which can be efficiently solved using convex solvers. Subsequently, a deep RL network is designed to optimize the TOTP results, where efficient learning is achieved in the solution space, thereby guaranteeing practical reliability and strong robustness via online interaction in applications. In addition, by incorporating convex optimization and learning techniques, the gap between simulation and experiment is successfully bridged, where the physical feasibility and efficient learning are ensured in the framework. Finally, comparative simulations and experimental results are included to show the effectiveness of the proposed strategy.

Fast trajectory planning and control of a lab-scale 3D gantry crane for a moving target in an environment with obstacles

In this work, the real-time optimal trajectory planning, together with a cascaded tracking controller, is presented for a three-dimensional (3D) gantry crane in an environment with static obstacles and a dynamically moving target considering dynamic constraints and control input limits. State-of-the-art trajectory optimization-based approaches require long computation times and cannot quickly respond to changes in the target state. The focus of this paper lies on a novel trajectory planning algorithm, which consists of two steps. First, an offline trajectory planner is implemented to compute a time-optimal, collision-free, and dynamically feasible trajectory database that connects all possible initial states of the gantry crane from a predefined starting subspace to the target states in a target subspace. Second, based on linear constrained quadratic programming, the online trajectory replanner makes use of this trajectory database to generate an optimal trajectory in real time that accounts for all changes in the target state. Additionally, a trajectory tracking controller is developed to take into account the dynamic constraints of the gantry crane and to compensate for possible model inaccuracies, disturbances, and other non-modeled effects. Both simulation and experimental results are presented to demonstrate the performance of the proposed trajectory (re)planning algorithm and the control concept.

Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness

The trajectory planning of UAV with nonholonomic constraints is usually taken as differential algebraic equation to solve the optimal control problem of functional extremum under the condition of inequality constraints. However, it can be challenging to meet the requirements of real-time for the high complexity. A differential flat theory based on B-spline trajectory planning can replace the optimal control problem with nonlinear programming and be a good means to achieve the efficient trajectory planning of an UAV under multiple dynamic constraints. This research verifies the feasibility of this theory with actual flight experiments.

Real-time jerk-minimization trajectory planning of robotic arm based on polynomial curve optimization

This paper deals with the jerk-minimization trajectory planning of robotic arms, in order to meet the increasing demands of the practical tasks that require fast motion planning of highly dynamic real-time movements for the task execution, by means of polynomial curve-based trajectory design. By solving a constrained quadratic optimization problem, the trajectory planning is optimized by minimizing the jerk of the robot end-effector. Experimental pick-and-place operations are carried out in comparison with the trajectory design without optimization and non-uniform rational B-spline (NURBS) curve, respectively, from which the results show the trajectory optimization is applicable in real-time trajectory planning. Both the numerical simulation and experimental implementations validate the presented approach of optimizing trajectory planning and show the effectiveness.

Real-time time-optimal continuous multi-axis trajectory planning using the trajectory index coordination method

Real-time time-optimal trajectory planning exists in a wide range of applications such as computer numerical control (CNC) manufacturing, robotics and autonomous vehicles. Generally, the methods to generate time-optimal trajectory can be categorized as non-real-time methods and real-time methods. Non-real-time methods such as direct optimization method tend to generate time-optimal trajectory through nonlinear or linear programming while it is computationally prohibitive for high frequency real-time applications. Current real-time methods are computationally efficient but either deal with the sparse waypoint trajectories or sacrifice the time optimality a lot. This paper innovatively proposed a time-optimal switching trajectory index coordination (TOS-TIC) framework to solve the real-time time-optimal planning problem for continuous multi-axis trajectories. The proposed method is able to generate time-optimal trajectory for continuous geometric paths while considering the axial velocity and acceleration constraints. The time-optimality of the trajectory planned by TOS-TIC is nearly the same as the offline planned optimal results. Meanwhile, the proposed method is computationally efficient for even 5kHz real-time applications. The main idea of TOS-TIC is coordinating several one-axis time-optimal switching controls to generate a modified control that decreases the state deviation from the desired trajectory. Several comparative experiments are carried out on an industrial biaxial linear motor stage. And the experimental results consistently verify that the proposed TOS-TIC real-time planner generates faster trajectory compared with the real-time lookahead method. In addition, the trajectory running time and final tracking error of the proposed method are nearly the same as the offline direct optimization method.

Dynamical repulsive fractional potential fields in 3D environment

Unmanned Aerial Vehicle applications have highly increased in the last years, from surveillance, exploration, rescue to transport applications. UAVs are more and more autonomous, therefore real-time trajectory planning is necessary and can be achieved thanks to artificial potential fields. The classic Ge & Cui repulsive force solely allows taking into account the velocity of the obstacles without any distinction. The Weyl potential force associates a degree of danger with an obstacle and has enabled to distinguish between the obstacles but the obstacle velocity is no more considered. Therefore, a new dynamical fractional repulsive force has been proposed by combining both advantages. The new dynamical fractional repulsive potential field is usable in a 3D environment and takes into account both the obstacle dynamics (position and speed) and their degree of dangerousness. Obstacle avoidance robustness is guaranteed, both from a safety point of view and from a trajectory optimization point of view. The proposed repulsive potential fields are first of all dynamical as they are based on the relative position and speed of the UAV in relation to the obstacle positions and speeds. Moreover, the dangerousness of the obstacles is also considered by introducing a fractional degree in their definition. Simulations results are provided to compare different repulsive potential field method (Ge & Cui, Weyl methods) to the proposed dynamical fractional potential field both in static and dynamical environments.

Minimum-Time Trajectory Planning for a Differential Drive Mobile Robot Considering Non-slipping Constraints

We propose a real-time minimum-time trajectory planning strategy with obstacle avoidance for a differential-drive mobile robot in the context of robot soccer. The method considers constraints important to maximize the system’s performance, such as the actuator limits and non-slipping conditions. We also present a novel friction model that regards the imbalance of normal forces on the wheels due to the acceleration of the robot. Theoretical guarantees on how to obtain a minimum-time velocity profile on a predetermined parametrized curve considering the modeled constraints are also presented. Then, we introduce a nonlinear, non-convex, local optimization using a version of the Resilient Propagation algorithm that minimizes the time of the curve while avoiding obstacles and respecting system constraints. Finally, employing a new proposed benchmark, we verified that the presented strategy allows the robot to traverse a cluttered field (with dimensions of 1.5 m $$\times $$ 1.3 m) in 2.8 s in 95% of the cases, while the optimization success rate was 85%. We also demonstrated the possibility of running the optimization in real-time, since it takes less than 13.8 ms in 95% of the cases.

Attitude-Constrained Time-Optimal Trajectory Planning for Rotorcrafts: Theory and Application to Visual Servoing

In this article, a novel real-time time-optimal trajectory planning (TOTP) approach is proposed for rotorcrafts under velocity constraints and complex nonconvex thrust, attitude input constraints. Different from existing works, the proposed method is the first real-time TOTP solution for rotorcrafts subject to velocity constraints and these nonconvex input constraints. The key insight is to transform the thrust and attitude constraints into the inequality constraints on the quadratic nonlinear function of the path parameter acceleration and the squared velocity, by exploiting the differential flatness characteristic of the rotorcraft. As a result, the constraints can be formulated as the problem of jointly solving analytical quadratic inequalities. On this basis, a path acceleration calculation algorithm is proposed to obtain the backward and forward acceleration profiles. In addition, by formulating the well-known field of view (FOV) constraints into the attitude constraints, the proposed framework can further guarantee the FOV constraint for visual servoing of rotorcrafts. Comparative experimental results are presented to show the superior performance of the proposed approach when compared with the second-order cone programming approach. In addition, some visual servoing experiments are conducted to demonstrate the capability of the proposed method to guarantee the FOV constraint.