Trajectory Planning Algorithms Research Articles

The Fitting of a Fiber-Reinforced-Plastic Complex Curved Surface and Its Orbit Optimization Model with Belt Grinding Line Contact.

The surface quality and profile accuracy of a radar fiberglass radome are determined by the manufacturing of the fiber-reinforced-plastic (FRP) complex curved mold. The surface quality, thickness uniformity, and shape accuracy of the mold seriously affect the temperature and deformation control during the manufacturing process of the radome, thus affecting the antenna’s serviceability, including its wave permeability and stability. Abrasive belt grinding is an effective method for processing FRP materials. However, issues regarding the profile fitting of the abrasive belt section line contact state and its influence on the precision of complex curved surfaces have not been solved, which seriously affects the processing quality. Here, an FRP complex curved surface mold surface based on the least-squares method was established. The local two-dimensional line contact and profile contour trajectory were obtained by the algorithm of optimal trajectory planning. Based on this, a grinding experiment was carried out. The experiments showed that the surface roughness based on this method was reduced from 0.503 to 0.289 μm, and the contour accuracy was improved by 16.9% compared with the conventional error. Through our analysis, the following conclusions can be drawn: the algorithm can effectively solve the problem of line contact surface fitting and significantly improve the precision of an FRP complex surface.

Special Issue: Highlights From ASME CIE 2018

Special Issue: Highlights From ASME CIE 2018

Design of a Cooperative V2V Trajectory-Planning Algorithm for Vehicles Driven on a Winding Road With Consideration of Human Drivers’ Characteristics

A vehicle-to-vehicle (V2V) cooperative trajectory-planning algorithm for connected vehicles driven on a winding road considering characteristics of human drivers is presented in this paper. The algorithm of cooperative game is introduced to plan collision-free trajectories for the involved encountering vehicles, with satisfaction of the safety requirements including vehicle stability and road-departure avoidance. The trajectory-planning algorithm is then converted to a Model Predictive Control (MPC) problem and solved with the concept of Pareto Optimality. The algorithm is compared with a V2V trajectory-planning algorithm with non-cooperative game. Simulations are conducted in the scenarios of lane-exchange on arc shaped roads with different radius to verify the proposed algorithm. Results show that the algorithm can accomplish the task of trajectory-planning on either winding road or straight road successfully, considering the driver's characteristics. The difference of collaboration tendency in V2V driving between using cooperative algorithm and non-cooperative algorithm is also studied and described.

Computer-assisted needle trajectory planning and mathematical modeling for liver tumor thermal ablation: A review.

Radiofrequency ablation (RFA) and microwave ablation (MWA) have become an important means for treating liver tumors. RFA and MWA are a minimally invasive therapy which involves an ablation applicator or needle (i.e., radiofrequency electrode or microwave antenna) inserted percutaneously into a tumor under the guidance of medical imaging, so as to destroy the tumor in situ by heating-induced coagulation necrosis. Treatment planning, particularly needle trajectory planning, is crucial to RFA and MWA. In clinical procedures, however, needle trajectory planning still relies on the personal experience of clinicians. Manual needle trajectory planning is tedious and may cause inter-operator difference. Therefore, computer-assisted needle trajectory planning techniques are of clinical value and have been extensively explored. However, a literature review that focuses on computer-assisted needle trajectory planning for liver tumor RFA and MWA has not been reported. In this paper, we conducted an extensive review on computer-assisted needle trajectory planning for RFA and MWA of liver tumors. Fundamentals of needle trajectory planning are summarized. Algorithms for single-needle and multi-needle trajectory planning are analyzed. Shortcomings of current computer-assisted needle trajectory planning algorithms are discussed and future developments are suggested.

Fast and Low-Cost Testing of Advanced Driver Assistance Systems using Small-Scale Vehicles

Abstract This article presents a small-scale testbed for automated driving. The main benefits of small-scale testing are safety, affordable hardware, and independence of traffic regulations and test tracks. The testbed using model trucks (scale 1:14) and model cars (scale 1:10) is described in detail and exemplary results using different advanced driver assistance systems are presented. The focus in this work lies on control engineering topics such as trajectory planning, tracking, prediction and estimation algorithms.

A New Trajectory-Planning Beetle Swarm Optimization Algorithm for Trajectory Planning of Robot Manipulators

Based on a heuristic optimization algorithm, this paper proposes a new algorithm named trajectory-planning beetle swarm optimization (TPBSO) algorithm for solving trajectory planning of robots, especially robot manipulators. Firstly, two specific manipulator trajectory planning problems are presented as the practical application of the algorithm, which are point-to-point planning and fixed-geometric-path planning. Then, in order to verify the effectiveness of the algorithm, this paper develops a control model and conducts numerical experiments on two planning tasks. Moreover, it compares with existing algorithms to show the superiority of our proposed algorithm. Finally, the results of numerical comparisons show that algorithm has a relatively faster computational speed and better control performance without increasing computational complexity.

High-precision trajectory tracking design and simulation for six degree of freedom robot based on improved active disturbance rejection control

High-precision trajectory tracking control is an important factor in the performance of industrial robots. In this study, a high-precision trajectory tracking strategy was proposed for controlling a degree of freedom serial robot on the basis of improved active disturbance rejection control. An independent control strategy of a single joint was adopted, and the corresponding decoupling control law was designed. An attitude trajectory-planning algorithm based on the circular-blending quaternion curve was improved. The position and attitude trajectories were transformed into the joint trajectory by using a kinematics equation and inverse velocity Jacobian matrix. The above-mentioned transformation link was used as a preprocessing link of the active disturbance rejection control, which is used for replacing the tracking differentiator of a typical active disturbance rejection control to eliminate the effect of the tracking delay. An experimental simulation was conducted by combining MATLAB and ADAMS. Simulation results show that the proposed control strategy can perform the tracking control of a task-space trajectory. The tracking precision of position and attitude trajectories were 0.01 mm and 0.01 s, respectively.

Trajectory planning and tracking control for towed carrier aircraft system

As an efficient and safe dispatching scheme is of great importance to ensure the effectiveness and safety of personnel on the Aircraft Carrier, and the towed aircraft system without bar is a common means of dispatching, the dispatching of the system is a significance and interesting question. In this paper, the towed carrier aircraft system without bar is transformed into a tractor–trailer system, and the nonlinear motion constraint is proposed. In order to improve the efficiency and safety of dispatching, the trajectory-planning and tracking of the system are studied, respectively. Obstacles in the environment and the nonlinear motion constraints are taken into consideration, the trajectory-planning is transformed into the optimal control problem, and combined with the symplecticity and pseudospectral method, an offline optimal control algorithm with high efficiency is proposed firstly. In order to accurately track the obtained trajectory, an online tracking method is proposed based on the receding horizon control (RHC) theory and the offline optimal control algorithm. Finally, the offline trajectory-planning algorithm has been proved by simulation experiment, it shows that the algorithm has high computational efficiency and good applicability. And the system can track the standard trajectory, even though there are disturbances in the environment, with high precision using the online tracking method, the calculation efficiency is also verified, and real-time tracking can be achieved.

Fast velocity trajectory planning and control algorithm of intelligent 4WD electric vehicle for energy saving using time‐based MPC

For intelligent four-wheel-drive (4WD) electric vehicle (EV), the vehicle speed can be planned and controlled for energy saving based on the slope information of road ahead. To reduce the calculation load of the optimisation algorithm, the model predictive control (MPC) method is formulated based on the time horizon in this study. Furthermore, a fast gradient method based control tool-GARMPC is used to solve the optimisation problem. First, the longitudinal dynamics model of 4WD EV based on time horizon and distance horizon is established based on the road slope information, respectively. Second, the MPC problem based on the time-discrete model is formulated and solved by GARMPC tool. For comparison, a dynamic program (DP) control method is introduced based on the distance-discrete model. Finally, the simulation is conducted under a designed road condition and a real measured road condition. The results show that the time-horizon based MPC method can significantly reduce the energy consumption compared with the proportion integration differentiation control method, which is similar to the driver's operation. Compared with the DP optimisation method, the time-based MPC method reduces the calculation time to smaller than 1 ms, which is essential for real-time application in a road vehicle.

Compensation of base disturbance using optimal trajectory planning of dual-manipulators in a space robot

This paper presents a trajectory planning algorithm for a space robot with dual-manipulators. Here one manipulator of the space robot captures a target, and another manipulator is free. In this case, this study uses one manipulator as the mission manipulator to capture the target, and another as the balance manipulator aiming at the compensation of the pose disturbance. For this method, a novel trajectory planning algorithm applied to the balance manipulator is presented. The trajectory planning problem is transformed into series of problems of the optimal state solution, and then the iterative algorithms for the trajectory planning are designed. In the iterative algorithms, the bias force on the spacecraft base caused by the balance manipulator is used as the compensation force. Then, to calculate the expected compensation force and torque, a pose control law for the spacecraft base is introduced. The expected compensation force and torque provide equality constraints for optimization problems, which implies that the trajectory planning algorithm compensates for not only the disturbance generated by the manipulator’s motion, but also environmental disturbances. This is because the expected compensation force and torque depend on the pose change of the spacecraft base rather than the type of the disturbance. Numerical simulation was carried out to analyze the proposed trajectory planning method. It was observed that the method greatly reduces the disturbance of Manipulator A on the spacecraft base. These results validated the effectiveness of the proposed method for the trajectory planning to make the spacecraft base disturbance up to minimum.

Active collision algorithm for autonomous electric vehicles at intersections

Various studies have been conducted on resisting network attacks on autonomous vehicles and vehicular networks. Invaded vehicles may cause severe damage and casualties; thus, it is essential to stop these vehicles to prevent traffic accidents and terrorist attacks. To improve traffic safety, an active collision algorithm based on trajectory planning is therefore proposed. The algorithm can be used to cause autonomous vehicles to collide with invaded vehicles at intersections. Several types of trajectory planning algorithms have been proposed for autonomous vehicles in recent years. However, a few of these algorithms consider active collisions with other vehicles. The main advantage and novelty of the proposed method are that it can be utilised to plan a suitable trajectory for active collision with invaded vehicles at intersections. This capability has rarely been discussed in the literature to date. The main contributions of this study are that the problem of active collision of autonomous vehicles at intersections is discussed and an effective active collision algorithm based on trajectory planning is proposed. The performance of the algorithm is demonstrated using simulation. The results show that the proposed algorithm is effective in enabling autonomous electric vehicles to collide with invaded vehicles at intersections.

A non-cooperative vehicle-to-vehicle trajectory-planning algorithm with consideration of driver’s characteristics

This paper presents a non-cooperative vehicle-to-vehicle trajectory-planning algorithm with consideration of the characteristics of different drivers. The driver–vehicle model considering vehicle dynamics and characteristics of the drivers is used to formulate a vehicle-to-vehicle encountering system. A non-cooperative control algorithm considering each of the driver–vehicle system as a player is employed to plan collision-free trajectories for the encountering vehicles with respective initial driving intentions. The non-cooperative problem is solved with the theory of Nash equilibrium and is ultimately converted to a standard nonlinear Model Predictive Control problem. Simulations are conducted in the scenarios of the lane-exchanging and overtaking with different initial vehicle speeds to verify the effectiveness of the proposed algorithm. Results show that the algorithm can accomplish the trajectory-planning task with consideration of both the safety requirement and the characteristics of drivers. The simulation results also show that the proposed algorithm has effectiveness for trajectory planning in different vehicle-to-vehicle encountering scenarios.

Complete and Time-Optimal Path-Constrained Trajectory Planning With Torque and Velocity Constraints: Theory and Applications

Time optimality and completeness are desired properties for robot trajectory planning, which ensure that robotic systems work reliably and efficiently. However, there is great difficulty to design planning algorithms that simultaneously guarantee time optimality and completeness. In this paper, a complete, time-optimal and real-time algorithm for path-constrained trajectory planning is proposed under both torque and velocity constraints. The time optimality and completeness of the proposed algorithm are theoretically proven with rigorous mathematical analysis. Moreover, the proposed approach is general and applicable on different robotic systems, and two examples are given on a two-link manipulator and an active-caster-based omnidirectional wheeled mobile robot. Comparative simulation and experimental results are provided to demonstrate the superior performance of the proposed algorithm.

Trajectory planning algorithm and simulation of 6-DOF manipulator

In order to solve the problem of joint acceleration mutation in the cubic polynomial trajectory planning algorithm, the algorithm of the quintic polynomial trajectory planning is studied. The results show that the calculation of quintic polynomial trajectory planning algorithm is relatively heavy, and it can ensure the continuity of angular acceleration and stable operation of motor. Trajectory planning is carried out in Cartesian space by using the spatial line and the spatial arc interpolation algorithm. MATLAB robotics toolbox is used to model the motion system and simulate the motion, which verifies the correctness and feasibility of the linear interpolation and circular interpolation algorithm.

Trajectory planning algorithm and simulation of 6-DOF manipulator

In order to solve the problem of joint acceleration mutation in the cubic polynomial trajectory planning algorithm, the algorithm of the quintic polynomial trajectory planning is studied. The results show that the calculation of quintic polynomial trajectory planning algorithm is relatively heavy, and it can ensure the continuity of angular acceleration and stable operation of motor. Trajectory planning is carried out in Cartesian space by using the spatial line and the spatial arc interpolation algorithm. MATLAB robotics toolbox is used to model the motion system and simulate the motion, which verifies the correctness and feasibility of the linear interpolation and circular interpolation algorithm.

Research on Trajectory Planning of 6-DOF Cutting-robot in Machining Complex Surface

It is important and difficult for the complicated surface processing in mechanical industry. In this paper, an improved algorithm for trajectory planning is proposed in impeller surface processing by using 6-DOF cutting-robot. Taking a single finished path of the impeller blade as an example, the feedrate of the cutter, bow height error, cutter-orientation and position are planned by the B-spline interpolation algorithm, the best cutting trajectory is obtained. On the basis of trajectory planning, the optimal movement scheme of 6-DOF cutting-robot joints is obtained, the 6-DOF cutting-robot feedrate and trajectory smooth transition is achieved and the joints movement adaptive adjustment is completed. Finally, the angles, the angular velocitys of the joints and their interrelated properties are analyzed. The research works indicate that the robot joint angle curves are continuous and stable, which has met the requirements of smooth movement of the robot, and the results show that the trajectory planning is effective and practical.

Mapping Accuracy of Trajectories of Manipulator Motion

The paper presents the algorithm for trajectory planning and the analysis of motion accuracy of an anthropomorphic manipulator whose the end-effector moves over the rectilinear-arc path. The path consists of two rectilinear segments of intersecting directions coupled with the arc of a fixed radius. On these rectilinear segments, the end-effector acceleration is described by a polynomial of 7th-degree. The motion over the arc proceeds at a constant velocity. The dynamic analysis was carried out on the basis of Lagrange’s equations of the second order. Manipulator flexibility and damping were considered according to the Kelvin-Voigt model introducing spring-damping components into the drive system. The simulation test results were presented in the form of spatial courses of the pre-assigned and realized trajectories as well as time courses of trajectory end-effector mapping errors for three paths with different radii of the arc.

Trajectory-Planning of Arrival Aircrafts Aiming at Adjustment of Separation and Fair Sharing of Noise by Aircraft Vectoring

The increasing amount of air traffic has escalated both the damage caused by aircraft noise and the workload on air traffic controllers. Future air traffic control systems are expected to ensure a fair distribution of aircraft noise to reduce the damage per capita. In this paper, we propose an automatic trajectory-planning algorithm that disperses arriving trajectories simultaneously with adjusting arrival time and avoiding other aircrafts during flight to reduce the noise per capita on the ground surrounding the arrival route. This method estimates the noise on the ground by identifying in advance ground points at one kilometer intervals. Each ground point has a noise index that is calculated by a weight and a sound propagation model for every aircraft trajectory. The proposed method also estimates the time of arrival of each aircraft and adjusts the error from the required time of arrival to zero by making detours or shortcuts from the nominal route. It also considers other aircrafts and avoids confliction during flight by making detours.

Teaching Joint-Level Robot Programming with a New Robotics Software Tool

With the rising popularity of robotics in our modern world there is an increase in the number of engineering programs that offer the basic Introduction to Robotics course. This common introductory robotics course generally covers the fundamental theory of robotics including robot kinematics, dynamics, differential movements, trajectory planning and basic computer vision algorithms commonly used in the field of robotics. Joint programming, the task of writing a program that directly controls the robot’s joint motors, is an activity that involves robot kinematics, dynamics, and trajectory planning. In this paper, we introduce a new educational robotics tool developed for teaching joint programming. The tool allows the student to write a program in a modified C language that controls the movement of the arm by controlling the velocity of each joint motor. This is a very important activity in the robotics course and leads the student to gain knowledge of how to build a robotic arm controller. Sample assignments are presented for different levels of difficulty.

Piezoelectric kinematic pairs with several DOF in miniature high-resolution piezoelectric robots

This paper presents results on the development and investigation of new miniature robots with increased number of degrees of freedom, based on the application of piezoelectric kinematic pairs with multi-DOF. The schematics of technologically advanced multi-DOF active kinematic pairs are presented and the details of their control are explained. The structure control of multi-DOF active kinematic pairs is based on sectioning of electrodes of the piezoelectric actuators and allows selecting desirable types of oscillations and speeds of links. Three modifications of piezoelectric robots with 6 and 15 DOFs are provided, together with their resolutions and responses to step inputs. Modal and harmonic analyses were performed and displacements of contact points were obtained. Trajectory planning algorithms are developed based on the numerical results.