Online Trajectory Planning Research Articles

How optimal is the minimum-time manoeuvre of an artificial race driver?

Minimum-lap-time optimal control problems (MLT-OCPs) are a popular tool to assess the best lap time of a vehicle on a racetrack. However, MLT-OCPs with high-fidelity dynamic vehicle models are computationally expensive, which limits them to offline use. When using autonomous agents in place of an MLT-OCP for online trajectory planning and control, the question arises of how far the resulting manoeuvre is from the maximum performance. In this paper, we improve a recently proposed artificial race driver (ARD) for online trajectory planning and control, and we compare it with a benchmark MLT-OCP. The novel challenge of our study is that ARD controls the same high-fidelity vehicle model used by the benchmark MLT-OCP, which enables a direct comparison of ARD and MLT-OCP. Leveraging its physics-driven structure and a new formulation of the g-g-v performance constraint, ARD achieves lap times comparable to the offline MLT-OCP (few milliseconds difference). We analyse the different trajectories resulting from the ARD and MLT-OCP solutions, to understand how ARD minimises the effect of local execution errors in search of the minimum-lap-time. Finally, we show that ARD consistently maintains its performance when tested on unseen circuits, even with unmodelled changes in the vehicle's mass.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Online Trajectory Planning for Parafoil First-Stage Booster System in Complex Wind Field

The parafoil has excellent gliding ability and operability for recovery of the first-stage booster, which makes the landing point of the first-stage booster controllable. However, during the recovery process, the wind field changes in real time due to changes in altitude and turbulent wind, which has a great influence on the trajectory and landing point of the parafoil recovery system. In order to realize accurate homing of the parafoil first-stage booster combination (PFC) in a complex wind field, an online trajectory planning algorithm based on the quartic Bézier curve is proposed in this paper. This algorithm combines the Bézier curve with the multiphase homing method and proposes a method to calculate the control points of the Bézier curve according to the time-varying wind field. First, a six-degrees-of-freedom model of the PFC is established, and the motion characteristics of the PFC are analyzed. Then, the drift of the PFC caused by the wind field is calculated, and it is superimposed on the target landing point to obtain the virtual landing point. On this basis, the quartic Bézier curve is used to plan the homing trajectory. The simulation results show that the algorithm has high computational efficiency for online trajectory planning. It can realize accurate homing of the PFC in complex wind fields with continuous unilateral brake deflections, which makes it conducive to practical application.

An Optimization-Based High-Precision Flexible Online Trajectory Planner for Forklifts

There are numerous prospects for automated unmanned forklifts in the fields of intelligent logistics and intelligent factories. However, existing unmanned forklifts often operate according to offline path planning first followed by path tracking to move materials. This process does not meet the needs of flexible production in intelligent logistics. To solve this problem, we proposed an optimized online motion planner based on the output of the state grid as the original path. Constraints such as vehicle kinematics; dynamics; turning restriction at the end of the path; spatial safety envelope; and the position and orientation at the starting point and the ending point were considered during path optimization, generating a precise and smooth trajectory for industrial forklifts that satisfied non-holonomic vehicle constraints. In addition, a new rapid algorithm for calculating the spatial safety envelope was proposed in this article, which can be used for collision avoidance and as a turning-angle constraint term for path smoothing. Finally, a simulation experiment and real-world tray-insertion task experiment were carried out. The experiments showed that the proposal was effective and accurate via online motion planning and the tracking of automated unmanned forklifts in a complicated environment and that the proposal fully satisfied the needs of industrial navigation accuracy.

A Type II singularity avoidance algorithm for parallel manipulators using output twist screws

Parallel robots (PRs) are closed-chain manipulators with diverse applications due to their accuracy and high payload. However, there are configurations within the workspace named Type II singularities where the PRs lose control of the end-effector movements. Type II singularities are a problem for applications where complete control of the end-effector is essential. Trajectory planning produces accurate movements of a PR by avoiding Type II singularities. Generally, singularity avoidance is achieved by optimising a geometrical path with a velocity profile considering singular configurations as obstacles. This research presents an algorithm that avoids Type II singularities by modifying the trajectory of a subset of the actuators. The subset of actuators represents the limbs responsible for a Type II singularity, and they are identified by the angle between two Output Twist Screws. The proposed avoidance algorithm does not require optimisation procedures, which reduces the computational cost for offline trajectory planning and makes it suitable for online trajectory planning. The avoidance algorithm is implemented in offline trajectory planning for a pick and place planar PR and a spatial knee rehabilitation PR.

Probabilistic framework for reliable optimal design of gearboxes in general-purpose industrial robots considering random use conditions

AbstractA vertically articulated robot with 6-degrees of freedom (DoF), called a general-purpose robot, can perform a myriad of different tasks within a workspace. This paper newly presents a probabilistic framework for the reliable optimal design of gearboxes used in general-purpose industrial robots, which considers random use conditions. To account for random use conditions, the start and end positions of a single motion profile are described as the random variable, which is statistically modeled as a uniform distribution based on the assumption that we have no information about the robot use pattern. Then, each sample of the random variable is converted to the corresponding motion profile by using an on-line trajectory planner. Monte Carlo simulation is implemented for the uncertainty propagation analysis, due to the heuristic feature of the on-line trajectory planner. In the design optimization formulation, the peak torque constraint and maximum bending moment constraint are described in a probabilistic manner. The system-level lifetime is calculated by combining component scale factors. The effectiveness of the proposed framework is demonstrated by examining a case study of a gearbox size problem for a 6-DoF serial industrial robot. The benefits of this study are as follows: Firstly, the proposed framework can evaluate the performance considering random use conditions. Secondly, torque reliability and bending moment reliability are newly proposed to ensure the dynamic performance of an industrial robot. Thirdly, the system-level lifetime by combining component scale factors gives more user-oriented and intuitive measure in an industrial robot design.

Two-Step Online Trajectory Planning of a Quadcopter in Indoor Environments with Obstacles

This paper presents a two-step algorithm for online trajectory planning in indoor environments with unknown obstacles. In the first step, sampling-based path planning techniques such as the optimal Rapidly exploring Random Tree (RRT*) algorithm and the Line-of-Sight (LOS) algorithm are employed to generate a collision-free path consisting of multiple waypoints. Then, in the second step, constrained quadratic programming is utilized to compute a smooth trajectory that passes through all computed waypoints. The main contribution of this work is the development of a flexible trajectory planning framework that can detect changes in the environment, such as new obstacles, and compute alternative trajectories in real time. The proposed algorithm actively considers all changes in the environment and performs the replanning process only on waypoints that are occupied by new obstacles. This helps to reduce the computation time and realize the proposed approach in real time. The feasibility of the proposed algorithm is evaluated using the Intel Aero Ready-to-Fly (RTF) quadcopter in simulation and in a real-world experiment.

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

<p style='text-indent:20px;'>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.</p>

Dynamic Online Trajectory Planning for a UAV-Enabled Data Collection System

Due to the maneuverability and flexibility of unmanned aerial vehicles (UAVs), the UAV-enabled data collection systems for wireless sensor networks (WSN) have received widespread attention. However, the state-of-the-art UAV trajectory designs mainly focus on static environments, which are not applicable in the practical scenarios considered in this work, e.g., mobile nodes, decommissioning of existing nodes, and new emergency nodes. This article proposes a two-level deep reinforcement learning (DRL) framework to solve this challenge. The first-level deep neural network (DNN) is applied to model the dynamic changing environment. In the second level, we employ a deep Q-learning network to plan a trajectory online according to the environment features from the first level DNN. Besides, online trajectory planning is performed by a low-power UAV edge computing platform. To enable online planning on the power-constraint UAV edge-computing platform, all networks adopt a lightweight low-complexity optimization design. According to simulation results, the proposed system achieves higher data acquisition success rates when compared to existing state-of-the-art methods. We also perform field tests on the proposed UAV edge computing platform, which also demonstrates high data acquisition performance.

Autonomous trajectory planning method for hypersonic vehicles in glide phase based on DDPG algorithm

An autonomous optimal trajectory planning method based on the deep deterministic policy gradient (DDPG) algorithm of reinforcement learning (RL) for hypersonic vehicles (HV) is proposed in this paper. First, the trajectory planning problem is converted into a Markov Decision Process (MDP), and the amplitude of the bank angle is designated as the control input. The reward function of the MDP is set to minimize the trajectory terminal position errors with satisfying hard constraints. The deep neural network (DNN) is used to approximate the policy function and action-value function in the DDPG framework. The Actor network then computes the control input directly according to flight states. Using a limited exploration strategy, the optimal policy network would be considered fully trained when the reward value reached maximum convergence. Simulation results show that the policy network trained using a DDPG algorithm accomplishes 3-dimensional (3D) trajectory planning during the HV glide phase with high terminal precision and stable convergence. Additionally, the single step calculation time of the policy network occurs in near real time, which suggests great potential as an autonomous online trajectory planner. Monte Carlo experiments prove the strong robustness of the implementation of an autonomous trajectory planner under aerodynamic disturbances.

Velocity Constraints Based Approach for Online Trajectory Planning of High-Speed Parallel Robots

High-speed parallel robots have been extensively utilized in the light industry. However, the influence of the nonlinear dynamic characteristics of high-speed parallel robots on system’s dynamic response and stable operation cannot be ignored during the high-speed reciprocating motion. Thus, trajectory planning is essential for efficiency and stability from pick-and-place (PAP) actions. This paper presents a method for planning the equal-height pick-and-place trajectory considering velocity constraints to improve the PAP efficiency and stability of high-speed parallel robots. The velocity constraints in the start-and-end points can reduce vibration from picking and placing, making the trajectory more suitable to complex beltline situations. Based on velocity constraints, trajectory optimization includes trajectory smoothness and joint torque to optimize cycle time is carried out. This paper proposes an online trajectory optimization solution. By using back propagation (BP) neural networks, the solution is simplified and can be solved in real-time. Simulation and experiments were carried out on the SR4 parallel robot. The results show that the proposed method improves the efficiency, smoothness, and stability of the robot. This paper proposes an online trajectory planning method which is velocity constraints based and can improve the efficiency and stability of high-speed parallel robots. The work of this research is conducive to finely applying high-speed parallel robots.

Flexible online planning based residual space object de-spinning for dual-arm space-borne maintenance

De-spinning a Residual Space Object is an important premise for space-borne maintenance, especially when the relative pose between a chaser and a spinning object is inaccurate due to measurement errors. In this paper, an online trajectory planning strategy for Residual Space Object de-spinning mission under the dual-arm space robotic set-up is proposed. A novel method named Soft Recurrent Actor-Critic is formulated to plan a flexible dual-arm approaching strategy, wherein the minimum requirement of sensors are only two on-board cameras. The Recurrent Neural Network is introduced to cope with the measurement errors. Moreover, the collision limitation and the minimal joints torque variant constraint are taken into account in reward function design for safety concerns. The effectiveness of the proposed method is demonstrated in two simulations, results show that nearly 30 percent performance improvement over the two state-of-the-art methods was achieved.

Decentralized Navigation of a UAV Team for Collaborative Covert Eavesdropping on a Group of Mobile Ground Nodes

Unmanned aerial vehicles (UAVs) are increasingly applied to surveillance tasks, thanks to their excellent mobility and flexibility. Different from existing works using UAVs for video surveillance, this paper employs a UAV team to carry out collaborative radio surveillance on ground moving nodes and disguise the purpose of surveillance. We consider two aspects of disguise. The first is that the UAVs do not communicate with each other (or the ground nodes can notice), and each UAV plans its trajectory in a decentralized way. The other aspect of disguise is that the UAVs avoid being noticed by the nodes for which a metric quantifying the disguising performance is adopted. We present a new decentralized method for the online trajectory planning of the UAVs, which maximizes the disguising metric while maintaining uninterrupted surveillance and avoiding UAV collisions. Based on the model predictive control (MPC) technique, our method allows each UAV to separately estimate the locations of the UAVs and the ground nodes, and decide its trajectory accordingly. The impact of potential estimation errors is mitigated by incorporating the error bounds into the online trajectory planning, hence achieving a robust control of the trajectories. Computer-based simulation results demonstrate that the developed strategy ensures the surveillance requirement without losing disguising performance, and outperforms existing alternatives. Note to Practitioners—The paper is motivated by the covertness requirement in the radio surveillance (also called eavesdropping) by UAVs. In some situations, the UAV user (such as the police department) wishes to disguise the surveillance intention from the targets, and the trajectories of UAVs play a significant role in the disguising. However, the typical UAV trajectories such as standoff tracking and orbiting can easily be noticed by the targets. Considering this gap, we focus on how to plan the UAVs’ trajectories so that they are less noticeable while conducting effective eavesdropping. We formulate a path planning problem aiming at maximizing a disguising metric, which measures the magnitude of the relative position change between a UAV and a target. A decentralized method is proposed for the online trajectory planning of the UAVs based on MPC, and its robust version is also presented to account for the uncertainty in the estimation and prediction of the nodes’ states.

Workspace analysis and motion control strategy of robotic mine anchor drilling truck manipulator based on the WOA-FOPID algorithm

The manipulator is the key component of the anchor drilling robot to automatically complete the anchoring operation underground. Due to the complexity of its motion equation and the limitations of its control strategy, the real-time pose and the positioning accuracy of the manipulator are inferior, which seriously restricts the safety, efficiency, and speed of roadway excavation. In order to improve the positioning accuracy and realize the optimal efficiency of the manipulator, this article designs a manipulator structure with four degrees of freedom. With the help of the D-H method and the intelligent parameter setting method, this article carries out the basic theoretical research on the kinematics and the fractional order FOPID control algorithm of the manipulator of the mining roof bolter, and formulates a manipulator motion control strategy. At the same time, combined with numerical simulations and field experiments, we explore the robustness and control efficiency of the hydraulic system of the manipulator under the working conditions of a harsh environment and limited space, and reveal that the intelligent optimization algorithm can control the motion state of the manipulator more accurately and stably after the parameters of the fractional order FOPID controller are positively determined. This study effectively solved the dynamic model uncertainty caused by time-varying internal parameters and external loads of the hydraulic servo system, optimized and reconstructed the structure and motion coefficient parameters of the manipulator, and revealed the control mechanism of a precise spatial positioning and online trajectory planning of the hydraulic servo system of the manipulator. Compared with the traditional PID control algorithm, this algorithm has a faster response speed and better expected track tracking ability. This research lays a theoretical foundation for the precise positioning and automatic support of the manipulator, and also provides a reference for the design of similar motion control algorithms.

A Real-Time Reentry Guidance Method for Hypersonic Vehicles Based on a Time2vec and Transformer Network

In this paper, a real-time reentry guidance law for hypersonic vehicles is presented to accomplish rapid, high-precision, robust, and reliable reentry flights by leveraging the Time to Vector (Time2vec) and transformer networks. First, referring to the traditional predictor–corrector algorithm and quasi-equilibrium glide condition (QEGC), the reentry guidance issue is described as a univariate root-finding problem based on bank angle. Second, considering that reentry guidance is a sequential decision-making process, and its data has inherent characteristics in time series, so the Time2vec and transformer networks are trained to obtain the mapping relation between the flight states and bank angles, and the inputs and outputs are specially designed to guarantee that the constraints can be well satisfied. Based on the Time2vec and transformer-based bank angle predictor, an efficient and precise reentry guidance approach is proposed to realize on-line trajectory planning. Simulations and analysis are carried out through comparison with the traditional predictor-corrector algorithm, and the results manifest that the developed Time2vec and transformer-based reentry guidance algorithm has remarkable improvements in accuracy and efficiency under initial state errors and aerodynamic parameter perturbations.

Auto-Tuning of Controller and Online Trajectory Planner for Legged Robots

This letter presents an approach for auto-tuning feedback controllers and online trajectory planners to achieve robust locomotion of a legged robot. The auto-tuning approach uses an Unscented Kalman Filter (UKF) formulation, which adapts/calibrates control parameters online using a recursive implementation. In particular, this letter shows how to use the auto-tuning approach to calibrate cost function weights of a Model Predictive Control (MPC) stance controller and feedback gains of a swing controller for a quadruped robot. Furthermore, this letter extends the auto-tuning approach to calibrating parameters of an online trajectory planner, where the height of a swing leg and the robot’s walking speed are optimized, while minimizing its energy consumption and foot slippage. This allows us to generate stable reference trajectories online and in real time. Results using a high-fidelity Unitree A1 robot simulator in Gazebo provided by the robot manufacturer show the advantages of using auto-tuning for calibrating feedback controllers and for computing reference trajectories online for reduced development time and improved tracking performance.

Robotic system with programmable motion constraint for transurethral resection

We propose a tele-operated transurethral robotic system with programmable motion constraint for tissue resection. The system consists of a surgeon console with an interaction device, a 7-degree-of-freedom manipulator, and a surgical end-effector. The surgical end-effector holds a resectoscope with a motor driven mechanism to perform electrocautery. Instrumental motion with remote center-of-motion (RCM) constraint is important for transurethral procedures since the damage to the healthy structures can be minimized. A screw theory-based programmable RCM generator is proposed to map the inputs of the interaction device to the RCM manifold in the manipulator space. To achieve smooth real-time manipulator following control with RCM constraint, an online trajectory planner is presented. Experiments were performed to evaluate the motion precision and accuracy. The results show that both the RCM precision and accuracy were less than 1 mm. Ex-vivo experiments of robotic resection of soft tissue were also carried out. The results show that our robotic system could achieve instrumental manipulation and delicate cutting under the real-time control of a surgeon. Our robotic system could assist surgeons in performing transurethral procedures in a remote manner with potential advantages of being accurate, less laborious and clean.

Orbit-Injection Strategy and Trajectory-Planning Method of the Launch Vehicle under Power Failure Conditions

Aiming at the problem of autonomous decision making and trajectory planning (ADMTP) for launch vehicles under power failure conditions, the target degradation order strategy (TDOS) and the trajectory online planning method were studied in this paper. Firstly, the influence of power failure on the orbit-injection process was analyzed. Secondly, the TDOS was proposed according to the mission attribute, failure mode, and multi-payload combination. Then, an online planning method based on the adaptive target update iterative guidance method (ATU-IGM) and radial basis neural network (RBFNN) was proposed, where the ATU-IGM adopted the basic TDOS criterion for generating optimal orbit-injection samples and online guidance instructions, and the RBFNN was used for orbit-injection samples training and online generation of orbital missions. Finally, the comparative simulation analysis was performed under multi-failure conditions. The results showed that the TDOS proposed in this paper could meet the requirements of the mission decision making under different failures, target orbit types, orbit-injection methods, and payload compositions. The online trajectory-planning capability deviation was less than 5%, and the mission decision-making and trajectory-planning time were less than 10 ms. This study provides theoretical support for autonomous decision making and planning of space launch missions.

A Hierarchical Autonomous Driver for a Racing Car: Real-Time Planning and Tracking of the Trajectory

The aim of this study was to develop trajectory planning that would allow an autonomous racing car to be driven as close as possible to what a driver would do, defining the most appropriate inputs for the current scenario. The search for the optimal trajectory in terms of lap time reduction involves the modeling of all the non-linearities of the vehicle dynamics with the disadvantage of being a time-consuming problem and not being able to be implemented in real-time. However, to improve the vehicle performances, the trajectory needs to be optimized online with the knowledge of the actual vehicle dynamics and path conditions. Therefore, this study involved the development of an architecture that allows an autonomous racing car to have an optimal online trajectory planning and path tracking ensuring professional driver performances. The real-time trajectory optimization can also ensure a possible future implementation in the urban area where obstacles and dynamic scenarios could be faced. It was chosen to implement a local trajectory planning based on the Model Predictive Control(MPC) logic and solved as Linear Programming (LP) by Sequential Convex Programming (SCP). The idea was to achieve a computational cost, 0.1 s, using a point mass vehicle model constrained by experimental definition and approximation of the car’s GG-V, and developing an optimum model-based path tracking to define the driver model that allows A car to follow the trajectory defined by the planner ensuring a signal input every 0.001 s. To validate the algorithm, two types of tests were carried out: a Matlab-Simulink, Vi-Grade co-simulation test, comparing the proposed algorithm with the performance of an offline motion planning, and a real-time simulator test, comparing the proposed algorithm with the performance of a professional driver. The results obtained showed that the computational cost of the optimization algorithm developed is below the limit of 0.1 s, and the architecture showed a reduction of the lap time of about 1 s compared to the offline optimizer and reproducibility of the performance obtained by the driver.

Edge Computing Assisted Autonomous Flight for UAV: Synergies between Vision and Communications

Autonomous flight for UAVs relies on visual information for avoiding obstacles and ensuring safe collision-free flight. In addition to visual clues, safe UAVs often need connectivity with the ground station. In this article, we study the synergies between vision and communications for edge-computing-enabled UAV flight. By proposing a framework of edge computing assisted autonomous flight (ECAAF), we illustrate that vision and communications can interact with and assist each other with the aid of edge computing and offloading, and further speed up UAV mission completion. ECAAF consists of three functionalities that are discussed in detail: edge computing for 3D map acquisition, radio map construction from the 3D map, and online trajectory planning. During ECAAF, the interactions of communication capacity, video offloading, 3D map quality, and channel state of the trajectory form a positive feedback loop. Simulation results verify that the proposed method can improve mission performance by enhancing connectivity. Finally, we conclude with some future research directions.