Time-optimal Path Research Articles

Time-Optimal Path Planning of a Hybrid Autonomous Underwater Vehicle Based on Ocean Current Neural Point Grid

Path planning is the precondition for Hybrid Autonomous Underwater Vehicles (HAUV) to enter the submerged area to undertake a mission. The influence of ocean currents on HAUV should be further investigated to obtain a time-optimal path. The improved A* algorithm and the neural network model are employed in this paper to plan a time-optimal path for the vehicle. The HAUV in glider mode is capable of traveling forward mainly through the zigzag motion in vertical plane. Since the vehicle can only receive the command orders when it surfaces from the water, the path is expected to include a series of discrete waypoints in the water surface. At the same time, the presence of submerged riverbeds is also taken into account to avoid hazards for HAUVs when it navigates in the water. It can be demonstrated that ocean currents can be used to decrease the operating time. The comparison results of the two methods verify that the size of the map affects the calculation time. In addition, the neural node represented method surpasses the modified A* method, especially when the map is too large.

Efficient time-optimal path planning of AUV under the ocean currents based on graph and clustering strategy

Path planning is particularly important for Autonomous Underwater Vehicles (AUVs) in the marine environments. Due to the existence of flow fields, many conventional path planning methods are not effective. As the flow distributions vary slowly in large spatial scales, this paper considers the influence of static non-uniform vector field and studies the time-optimal path planning of AUV. The method proposed in this paper is called GK-OPM (Graph and K-means based Optimization Method). GK-OPM generates initial paths for minimum-time path optimization using digraph and K-means method, which benefit optimality and efficiency, respectively. To discuss the parameters in GK-OPM and compare the performance with genetic algorithm (GA) and particle swarm optimization (PSO), Monte Carlo simulation is carried out under the ocean currents simulated by the Lamb-vertex function. The feasibility is verified on discrete ocean data and three-dimensional environments, too. The results show that GK-OPM has about 6–8 times better efficiency than GA and PSO and maintains optimality at the same time.

Time-Optimal Online Replanning for Agile Quadrotor Flight

In this letter, we tackle the problem of flying a quadrotor using time-optimal control policies that can be replanned online when the environment changes or when encountering unknown disturbances. This problem is challenging as the time-optimal trajectories that consider the full quadrotor dynamics are computationally expensive to generate, on the order of minutes or even hours. We introduce a sampling-based method for efficient generation of time-optimal paths of a point-mass model. These paths are then tracked using a Model Predictive Contouring Control approach that considers the full quadrotor dynamics and the single rotor thrust limits. Our combined approach is able to run in real-time, being the first time-optimal method that is able to adapt to changes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on-the-fly</i> . We showcase our approach’s adaption capabilities by flying a quadrotor at more than 60 km/h in a racing track where gates are moving. Additionally, we show that our online replanning approach can cope with strong disturbances caused by winds of up to 68 km/h.

Heuristic decomposition planning for fast spacecraft reorientation under multiaxis constraints

Spacecraft are required to achieve fast attitude reorientation in many space missions. However, the attitude maneuver will be limited by the bounded and pointing constraints. The presence of these complex multiaxis constraints will largely reduce the feasible attitude space and greatly degrade the solving efficiency of the planning algorithm. For the time-optimal spacecraft reorientation problem under multiaxis constraints, a new heuristic decomposition planning on the virtual domain (HDPV) method is proposed in this paper. The parameterized attitude path is first determined on the virtual domain. Then the virtual-domain-based variable-step approach is presented to rapidly check the pointing constraints and generate the sets of candidate rotational-path decomposition nodes. The composite-position heuristics is developed to select the best node during the decomposition optimization, which considers the maneuver time and connection smoothness of paths. The total continuous parameterized path under keep-out and keep-in constraints is yielded through recursive planning. Finally, the time-optimal path parameterization approach is adopted to minimize the maneuver time along the total path and generate a fast attitude trajectory under bounded constraints on the time domain. Simulation results demonstrate the high computational efficiency and good optimization effect of the proposed method.

A Neural Network Model of Smart Aging Combining Family Structure Change Factors.

In this paper, we analyze the changes in family structure and explore the changes in detail, based on which we construct a neural network model of smart aging. Based on the gender perspective, the individual growth model in the multilayer linear model is used to examine the effects of family structure changes on the elderly in terms of economic exchange, daily care, and emotional support. The results show that there is no significant gender difference in the family structure changes on the elderly in terms of economic exchange and daily care, but there is a significant gender difference in terms of emotional support. To solve the problem of data imbalance in the daily activity categories of the elderly, this paper resamples the data and uses different neural network models for activity recognition of the sensor data generated from the daily activities of the elderly. In this paper, the daily behavior patterns of the elderly over a while are studied by correlating three conditions of time distance, optimal path, and sensor distance to discover the daily behavior patterns of the elderly, while the abnormal behavior patterns can be well separated by EM clustering algorithm. The daily behavior of the elderly is a coarse-grained representation of their daily activities. It is not limited to a specific activity and does not require the sensor ID, trigger time, and location triggered by the activity to be consistent, but in long-term daily activity data, it abstracts the general behavior rules of the elderly activities. Through the research of this paper, the existing system is improved, and the multifaceted needs of the elderly are fully considered, from housing needs to spiritual needs, to face the current elderly care problems with a positive attitude, create a good social elderly care environment for the elderly, and realize the real elderly care.

Numerical Simulation of Time-Optimal Path Planning for Autonomous Underwater Vehicles Using a Markov Decision Process Method

Many path planning algorithms developed for land or air based autonomous vehicles no longer apply under the water. A time-optimal path planning method for autonomous underwater vehicles (AUVs), based on a Markov decision process (MDP) algorithm, is proposed for the marine environment. Its performance is examined for different oceanic conditions, including complex coastal bathymetry and time-varying ocean currents, revealing advantages compared to the A* algorithm, a traditional path planning method. The ocean current is predicted using a regional ocean model and then provided to the MDP algorithm as a priori. A computation-efficient and feature-resolved spatial resolution are determined through a series of sensitivity experiments. The simulations demonstrate the importance to incorporate ocean currents in the path planning of AUVs in the real ocean. The MDP algorithm remains robust even if the ocean current is complex.

Time Optimal Trajectories for a Car-Like Mobile Robot

This article studies the time optimal paths of a car-like mobile robot navigating in an obstacle-free planar environment. The robot, with forward and backward speeds, is controlled by bounded acceleration and limited front-wheels steering rate. The article extends previous results that solved this problem for a simplified car-robot model controlled by bounded speed and limited heading rate. The simplified car-robot model forms a unicycle with coupled bounds on the control inputs, while the full car-robot model has independent control inputs. The problem is analyzed as an optimal control problem by the minimum principle and by singular control theory. While the simplified car-robot model gives six time optimal path primitives, the optimality conditions for the full car-robot model yield <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">twelve path primitives</i> that form the time optimal paths. Three primitives involve singular controls of the steering front wheels that asymptotically align the robot along a straight line motion. All path primitives are analytically characterized and representative examples are studied in order to demonstrate how the path primitives combine to form the time optimal paths.

An optimal control-based path planning method for unmanned surface vehicles in complex environments

This paper proposes an optimal control-based method named the rapid-Gauss pseudospectral method (RGPM) to obtain a smooth time-optimal path for unmanned surface vehicles (USVs). It is a general global path planning method, improving the Gauss pseudospectral method (GPM) which cannot be applied to complex ocean scenarios. In addition, we optimize the representation of obstacles and add a Maklink algorithm to reduce the computaitonal cost. More specifically, a unified obstacle modeling approach is first introduced, then a continuous-time-optimal-control path planning problem considering USV kinematics is formulated. The orthogonal collocation method is used to discretize the continuous-time-optimal control problem into a nonlinear programming (NLP) problem. Furthermore, we introduce a mesh refinement technique to achieve collision avoidance between adjacent discrete points. To enhance computational efficiency, an initialization and iteration approach is further proposed. Herein, a MAKLINK graph is established to obtain a suboptimal path as the initial guess for the NLP problem. Obstacle-avoidance constraints are iteratively updated according to whether or not there are collisions in the current path. The proposed method was compared with the traditional GPM under two different scenarios. The simulation results show that the proposed method is superior to the traditional GPM in terms of path quality and convergence speed and can obtain quasi-time-optimal paths under complex conditions simultaneously.

Sampling-Based Time-Optimal Path Parameterization with Jerk Constraints for Robotic Manipulation

Sampling-Based Time-Optimal Path Parameterization with Jerk Constraints for Robotic Manipulation

AlphaPilot: autonomous drone racing

This paper presents a novel system for autonomous, vision-based drone racing combining learned data abstraction, nonlinear filtering, and time-optimal trajectory planning. The system has successfully been deployed at the first autonomous drone racing world championship: the 2019 AlphaPilot Challenge. Contrary to traditional drone racing systems, which only detect the next gate, our approach makes use of any visible gate and takes advantage of multiple, simultaneous gate detections to compensate for drift in the state estimate and build a global map of the gates. The global map and drift-compensated state estimate allow the drone to navigate through the race course even when the gates are not immediately visible and further enable to plan a near time-optimal path through the race course in real time based on approximate drone dynamics. The proposed system has been demonstrated to successfully guide the drone through tight race courses reaching speeds up to {8},{hbox {m}/hbox {s}} and ranked second at the 2019 AlphaPilot Challenge.

Aircraft Parking Trajectory Planning in Semistructured Environment Based on Kinodynamic Safety RRT ∗

To improve the safety and effectiveness of autonomous towing aircraft aboard the carrier deck, this study proposes a velocity-restricted path planner algorithm named as kinodynamic safety optimal rapidly exploring random tree (KS-RRT ∗ ) to plan a near time-optimal path. First, a speed map is introduced to assign different maximum allowable velocity for the sampling points in the workspace, and the traverse time is calculated along the kinodynamic connection of two sampling points. Then the near time-optimal path in the tree-structured search map can be obtained by the rewiring procedures, instead of a distance-optimal path in the original RRT ∗ algorithm. In order to enhance the planner’s performance, goal biasing scheme and fast collision checking technique are adopted in the algorithm. Since the sampling-based methods are sensitive to their parameters, simulation experiments are first conducted to determine the optimal input settings for the specific problem. The effectiveness of the proposed algorithm is validated in several common aircraft parking scenarios. Comparing with standard RRT ∗ and human heuristic driving, KS-RRT ∗ demonstrates a higher success rate, as well as shorter computation and trajectory time. In conclusion, KS-RRT ∗ algorithm is suitable to generate a near time-optimal safe path for autonomous high density parking in semistructured environment.

Online time-optimal path and trajectory planning for robotic multipoint assembly

PurposeThe purpose of this paper is to propose an efficient path and trajectory planning method to solve online robotic multipoint assembly.Design/methodology/approachA path planning algorithm called policy memorized adaptive dynamic programming (PM-ADP) combines with a trajectory planning algorithm called adaptive elite genetic algorithm (AEGA) for online time-optimal path and trajectory planning.FindingsExperimental results and comparative study show that the PM-ADP is more efficient and accurate than traditional algorithms in a smaller assembly task. Under the shortest assembly path, AEGA is used to plan the time-optimal trajectories of the robot and be more efficient than GA.Practical implicationsThe proposed method builds a new online and efficient path planning arithmetic to cope with the uncertain and dynamic nature of the multipoint assembly path in the Cartesian space. Moreover, the optimized trajectories of the joints can make the movement of the robot continuously and efficiently.Originality/valueThe proposed method is a combination of time-optimal path planning with trajectory planning. The traveling salesman problem model of assembly path is established to transfer the assembly process into a Markov decision process (MDP). A new dynamic programming (DP) algorithm, termed PM-ADP, which combines the memorized policy and adaptivity, is developed to optimize the shortest assembly path. GA is improved, termed AEGA, which is used for online time-optimal trajectory planning in joints space.

Path planning for autonomous underwater vehicles based on interval optimization in uncertain flow fields

The predictive uncertainty of ocean currents needs to be considered in the path planning of autonomous underwater vehicles (AUV) in oceanic environments. An interval optimization (IO) scheme is presented in this paper to plan time-optimal paths for AUVs operating in oceanic environments with dynamic and uncertain flow fields; interval currents are established to process the uncertainty of forecasted ocean flows, and the IO scheme is used to search for time-optimal paths in the interval current fields. The IO scheme is a two-layer framework: In the outer layer, quantum-behaved particle swarm optimization is used to generate and optimize candidate paths. In the inner layer, the interval response of the candidate path from the outer layer is calculated under interval current fields, and they are converted into a time-optimal fitness value in accordance with the possibility degree of interval numbers. The influence of predictive uncertainty is analyzed via simulation, and the robustness of the IO scheme is verified.

A control parametrization based path planning method for the quad-rotor uavs

&lt;p style='text-indent:20px;'&gt;A time optimal path planning problem for the Quad-rotor unmanned aerial vehicles (UAVs) is investigated in this paper. A 3D environment with obstacles is considered, which makes the problem more challenging. To tackle this challenge, the problem is formulated as a nonlinear optimal control problem with continuous state inequality constraints and terminal equality constraints. A control parametrization based method is proposed. Particularly, the constraint transcription method together with a local smoothing technique is utilized to handle the continuous inequality constraints. The original problem is then transformed into a nonlinear program. The corresponding gradient formulas for both of the cost function and the constraints are derived, respectively. Simulation results show that the proposed path planning method has less tracking error than that of the rapid-exploring random tree (RRT) algorithm and that of the A star algorithm. In addition, the motor speed has less changes for the proposed algorithm than that of the other two algorithms.&lt;/p&gt;

Research on path selection system based on green transportation

The transportation sector already accounts for 14% of global greenhouse gas emissions. Therefore, controlling carbon emissions in the transportation sector has become a top priority for China and other countries around the world. In addition to the technological development of clean energy transportation, the most critical aspect of the globalization of new energy transportation industry and market is the optimization of access routes. This paper will be based on road travel time estimation and optimal path selection of energy efficient transportation research hotspots. Firstly, the accuracy of road travel time estimation is improved according to the basic law of traffic flow. At the same time, this paper defines the optimal route into two cases of shortest path and shortest time for solving. Finally, the actual solution process is given according to the actual problem, as well as the optimal route, aiming to promote the strong development in the field of intelligent navigation system and energy-efficient transportation.

Time Optimal Trajectories for a Mobile Robot With Acceleration and Speed Limits in the Presence of an Obstacle

Abstract This paper studies the time optimal paths of a mobile robot navigating in a planar environment containing an obstacle. The paper considers a point-mass robot that moves with bounded acceleration and limited turn-rate controls in the presence of an obstacle. The optimal control problem yields 12 path primitives that form the time optimal paths of the point-mass robot. The problem is then extended to a disc-robot that moves in the presence of an obstacle with turn in-place capability. The optimality conditions yield 12 modified path primitives that form the time optimal paths of the disc-robot. All path primitives are analytically characterized and examples demonstrate how they form time optimal trajectories in the presence of several obstacle types.

Time-optimal Path Planning of Multi-axis CNC Processes Using Variability of Orientation

In multi-axis processes, such as welding or 3D printing, the determination of the orientation of the tool relative to the workpiece is usually determined by technology-dependent geometric algorithms. In the simplest case, the orientation of the tool is defined according to the surface normal vectors of the workpiece surfaces. However, with large curvature gradients, this method can lead to jumps in the orientation which lead to unwanted stopping of the translational motion. In the linear interpolation of this movement, the path speed usually decreases significantly due to the relatively large compensating movement of a kinematic system. This type of path movement usually has negative effects on the CNC process, which requires constant path velocities.This paper describes a method for time-optimized path planning that utilizes the orientation tolerances of multi-axis processes. Orientation tolerances are process-dependent tolerances that indicate which orientation ranges (angular positions) from tool to workpiece are permissible without decreasing the process quality. The potential time savings of this method are shown with an extreme example of a planar 3-axis kinematics and on an industrial 7-axis CNC system.

Formation keeping method of weakly driven multi robot in time-varying flow field

In order to solve the problem that group formation control and optimal path cannot be considered simultaneously for weakly driven multi robot under the influence of environmental flow field, a method combining time-optimal path planning and leader-follower formation control is proposed in this paper. The time-optimal path of the leader is obtained by level set method, and the formation keeping is based on this path. According to the position of the leader and the reachable set of the follower at a certain time, the position of the follower is determined by solving the formation optimization function, and the complete path is completed by solving the formation optimization problem iteratively. While the formation optimization function maintains the group formation, the reachable set generated by the level set method ensures the feasibility of the path obtained in the time-varying strong flow.

Three-dimensional time-optimal path planning in the ocean

Autonomous underwater vehicles (AUVs) operate in the three-dimensional and time-dependent marine environment with strong and dynamic currents. Our goal is to predict the time history of the optimal three-dimensional headings of these vehicles such that they reach the given destination location in the least amount of time, starting from a known initial position. We employ the exact differential equations for time-optimal path planning and develop theory and numerical schemes to accurately predict three-dimensional optimal paths for several classes of marine vehicles, respecting their specific propulsion constraints. We further show that the three-dimensional path planning problem can be reduced to a two-dimensional one if the motion of the vehicle is partially known, e.g. if the vertical component of the motion is forced. This reduces the computational cost. We then apply the developed theory in three-dimensional analytically known flow fields to verify the schemes, benchmark the accuracy, and demonstrate capabilities. Finally, we showcase time-optimal path planning in realistic data-assimilative ocean simulations for the Middle Atlantic Bight region, integrating the primitive-equation of the Multidisciplinary Simulation Estimation and Assimilation System (MSEAS) with the three-dimensional path planning equations for three common marine vehicles, namely propelled AUVs (with unrestricted motion), floats (that only propel vertically), and gliders (that often perform sinusoidal yo-yo motions in vertical planes). These results highlight the effects of dynamic three-dimensional multiscale ocean currents on the optimal paths, including the Gulf Stream, shelfbreak front jet, upper-layer jets, eddies, and wind-driven and tidal currents. They also showcase the need to utilize data-assimilative ocean forecasts for planning efficient autonomous missions, from optimal deployment and pick-up, to monitoring and adaptive data collection.

Multi-Agent Motion Planning for Dense and Dynamic Environments via Deep Reinforcement Learning

This letter introduces a hybrid algorithm of deep reinforcement learning (RL) and Force-based motion planning (FMP) to solve distributed motion planning problem in dense and dynamic environments. Individually, RL and FMP algorithms each have their own limitations. FMP is not able to produce time-optimal paths and existing RL solutions are not able to produce collision-free paths in dense environments. Therefore, we first tried improving the performance of recent RL approaches by introducing a new reward function that not only eliminates the requirement of a pre supervised learning (SL) step but also decreases the chance of collision in crowded environments. That improved things, but there were still a lot of failure cases. So, we developed a hybrid approach to leverage the simpler FMP approach in stuck, simple and high-risk cases, and continue using RL for normal cases in which FMP can’t produce optimal path. Also, we extend GA3C-CADRL algorithm to 3D environment. Simulation results show that the proposed algorithm outperforms both deep RL and FMP algorithms and produces up to 50 $\%$ more successful scenarios than deep RL and up to 75 $\%$ less extra time to reach goal than FMP.