Trajectory Generation Algorithm Research Articles

Cubic spline trajectory generation with axis jerk and tracking error constraints

This paper presents a cubic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles for CNC machines with confined axis jerk and tracking error. A series of reference knots are connected using cubic spline functions in time t for constructing axis trajectories. They are generated in such a way that continuity up to the second derivative is preserved along the overall composite curve. For CNC machines governed by a typical PID controller, the tracking error is also constrained as well as the velocity, acceleration, and jerk for each axis. The time intervals between each pair of adjacent knots are scheduled such that the machining time is minimized subject to all the constraints. Experiment results are presented to illustrate the application of the algorithm.

An Algorithm for Generation of Coordinated Robot Trajectories in Cartesian Space

In the paper a trajectory generation algorithm for two robots’ coordinated motion is presented. Two instances of the algorithm, each for one robot, run in the same time and calculate trajectories’ position and orientation coordinates. Initial and end robots’ end-effectors poses are defined and values of linear and angular speeds are programmed. To minimize relative position and orientation errors an idea of corrective motion is introduced. Trajectory coordinates are calculated as the sum of programmed and corrective motion. The algorithm was implemented in a simulation environment and results of simulation are presented. Static accuracy analysis for general case and stability verification for fixed values of robots’ parameters are described. Finally, an outline of proposed procedure of building a virtual environment for reachability verification and collision checking is presented.

Contouring Controller for Precise Motion Control Systems

This paper discusses the trajectory generation algorithm, contour error construction method and finally the contour controller design. In the trajectory generation algorithm combination of elliptical Fourier descriptors (EFD) and time based spline approximation (TBSA) is used to generate position, velocity and acceleration references. Contour error is constructed using transformation of trajectory tracking errors. Transformation is computationally efficient and requires only reference velocity information. Contour controller is designed using sliding mode control. Experiments are performed on planar linear motion stage and significant contour error reduction is observed.

Aircraft Shortest and Fastest Continuous Descent Approach Development

Flight-path optimization is designed for minimizing aircraft noise and fuel consumption around airports and for increasing the number of aircraft operations. The main objective of this paper is to provide the optimal flight approach, taking into account noise sources, fuel consumption, constraints, and extreme operational limits of aircraft. This paper introduces a new trajectory generation algorithm based on Hamilton–Jacobi–Bellman considerations, taking into account aircraft jet noise. The shortest and fastest continuous descent approach is obtainedasanoptimaltrajectoryreducingaircraftnoise(6 dB)andfuelconsumption(27%to15%).Itisaonesegment approach with a soft and short continuous descent, which is better conceived in terms of reduction of environmental impacts of aircraft than the two-segment approach. Results show that this new method is appropriated for aircraft trajectory optimization and could be implemented in avionic systems. It can be interfaced with the in-flight management system respecting constraints of the airspace system regulation and improving its functionalities.Shortestandfastestcontinuousdescentapproachcouldbenefitbothairlinesandcommunities.Italso could be designed for practitioners to understand the implementation of airport management systems. Shortest and fastestcontinuousdescentapproachisconsideredasastrategytobeusedforthe finalapproach.Itallowsonetoavoid difficulties of the flight. It can help the flight crew to make timely and correct thrust settings and approach path corrections. Because this study is limited to one noise source for one aircraft, other research is needed to take into account all noise sources of several aircraft.

자동 발렛 파킹을 위한 횡방향 제어기 설계 및 차종변화에 대한 제어 성능 분석

The unified lateral control algorithm for automatic valet parking for various types of vehicles is presented and its feasibility is shown experimentally via field tests for the given parking scenario. First, a trajectory generation algorithm for forward driving and backward multi-step parking maneuvers is developed. Then, with consideration of different types of vehicles and operating conditions, a kinematic vehicle model is used and validated using field test data. Using the nonlinear vehicle model, the lateral controller is designed based on dynamic surface control. Finally the proposed lateral control law is validated via hardware-in-the-loop simulations for different types of vehicles and experimentally using a test vehicle through field tests.

An Intelligent Auto Parking System for Vehicles

Autoparking assistant systems are a new and very promising area in automotive systems engineering. Since the traffic in modern cities becomes more intense, it is getting harder for a driver. Those systems are necessary for an inexperienced one to find a proper parking slot, or to park in a narrow parking slot without damaging his car or the vehicles around. The implementation of autoparking assistant systems may reduce drivers' stress and make parking generally more comfortable. In addition, such system can be extremely useful for senior or disabled people or for drivers with reduced mobility. The implementation of autoparking assistant systems may increase the safety of the parking, and therefore the development of such systems is a highly-demanded task. We introduce an intelligent autoparking system that automatically generates trajectory for parking using a fuzzy logic. This paper consists of three parts. In first part we introduce trajectory generation method for parallel parking without collisions. Fuzzy-logic based trajectory generation algorithm is described in second part. Experimental results presented in the third part of the paper prove effectiveness of the proposed method.

차륜 이동 로봇의 모터 구동 전압 제한 조건을 고려한 코너링(cornering) 모션의 최소 시간 궤적 계획 및 제어

We propose time-optimal cornering motion trajectory planning and control algorithms for differential wheeled mobile robot with motor actuating voltage constraint, under piecewise constant control input condition. For time-optimal cornering trajectory generation, 1) we considered mobile robot's dynamics including actuator motors, 2) divided the cornering trajectory into one liner section, followed by two cornering section with angular acceleration and deceleration, and finally one liner section, and 3) formulated an efficient trajectory generation algorithm satisfying the bang-bang control principle. Also we proposed an efficient trajectory control algorithm and implemented with an X-bot to prove the performance.

An iterative linear quadratic regulator based trajectory tracking controller for wheeled mobile robot

We present an iterative linear quadratic regulator (ILQR) method for trajectory tracking control of a wheeled mobile robot system. The proposed scheme involves a kinematic model linearization technique, a global trajectory generation algorithm, and trajectory tracking controller design. A lattice planner, which searches over a 3D (x, y, θ) configuration space, is adopted to generate the global trajectory. The ILQR method is used to design a local trajectory tracking controller. The effectiveness of the proposed method is demonstrated in simulation and experiment with a significantly asymmetric differential drive robot. The performance of the local controller is analyzed and compared with that of the existing linear quadratic regulator (LQR) method. According to the experiments, the new controller improves the control sequences (ν, ω) iteratively and produces slightly better results. Specifically, two trajectories, ‘S’ and ‘8’ courses, are followed with sufficient accuracy using the proposed controller.

A Trajectory Generation Algorithm for Optimal Consumption in Electromagnetic Actuators

Camless internal combustion engines offer improvements over traditional engines in terms of torque performance, reduction of emissions, reduction of pumping losses and fuel economy. Theoretically, electromagnetic valve actuators offer the highest potentials for improving efficiency due to their control flexibility. For real applications, however, the valve actuators developed so far suffer from high power consumption and other control problems. One key point is the design of the reference trajectory to be tracked by the closed loop controller. In this brief, a design technique aimed at minimizing power consumption is proposed. A constrained optimization problem is formulated and its solution is approximated by exploiting local flatness and physical properties of the system. The performance of the designed trajectory is validated via an industrial simulator of the valve actuator.

자율주행 시스템의 장애물 회피 알고리즘에 관한 연구

In unmanned vehicles' navigation, the shapes of obstacles are generally irregular and complex. The motion of vehicles based on the range sensor system such as ultrasonic sensors or laser sensors can be unstable due to the irregular shape of the obstacles. In this case, to generate stable trajectory of unmanned vehicles equipped with range sensors, we need an approach that can simplify an obstacle's irregular shape information. In this paper, we propose the trajectory generation algorithm that an vehicle can stably navigate in the environments where irregular shaped obstacles are scattered. The proposed method is verified through the analysis of vehicle's trail and direction data acquired by simulations and implementations.

Novel Online Speed Profile Generation for Industrial Machine Tool Based on Flexible Neuro-Fuzzy Approximation

Reference trajectory generation is one of the most important tasks in the control of machine tools. Such a trajectory must guarantee a smooth kinematics profile to avoid exciting the natural frequencies of the mechanical structure or servo control system. Moreover, the trajectory must be generated online to enable some feed rate adaptation mechanism working. This paper presents the online smooth speed profile generator used in trajectory interpolation in milling machines. Smooth kinematic profile is obtained by imposing limit on the jerk—which is the first derivative of acceleration. This generator is based on the neuro-fuzzy system and is able to adapt online the current feed rate to changing external conditions. Such an approach improves the machining quality, reduces the tool wear, and shortens total machining time. The proposed trajectory generation algorithm has been successfully tested and can be implemented on a multiaxis milling machine.

Online Trajectory Generation for Mobile Robots with Kinodynamic Constraints and Embedded Control Systems

The paper describes trajectory generation and tracking control algorithms, respectively based on nonlinear filtering and dynamic feedback linearization, for mobile robots. A main feature of proposed algorithms is that they are suitable for the implementation on embedded systems with limited computational resources. The trajectory generator is based on nonlinear filters and logic-based management of reference inputs and dynamic constraints, allowing online smoothing of straight-line reference paths. Sparse via-points along a path can be assigned by a global planner based on obstacle avoidance algorithms and can be changed at any time during motion. Moreover, the trajectory generated by the nonlinear filter can be fed into a control loop based on the dynamic model of the robot, so that accurate tracking can be achieved. The paper includes practical remarks for efficient fixed-point implementation of the proposed trajectory generator.

Analysis of Tsai calibration method using two- and three-dimensional calibration objects

Camera calibration is a fundamental process for both photogrammetric and computer vision. Since the arrival of the direct linear transformation method and its later revisions, new methods have been developed by several authors, such as: Tsai, Heikkila and Zhang. Most of these have been based on the pinhole model, including distortion correction. Some of these methods, such as Tsai method, allow the use of two different techniques for determining calibration parameters: a non-coplanar calibration technique using three-dimensional (3D) calibration objects, and a coplanar technique that uses two-dimensional (2D) calibration objects. The calibration performed by observing a 3D calibration object has good accuracy, and produces very efficient results; however, the calibration object must be accurate enough and requires an elaborate configuration. In contrast, the use of 2D calibration objects yields less accurate results, is much more flexible, and does not require complex calibration objects that are costly to produce. This article compares these two different calibration procedures from the perspective of stereo measurement. Particular attention was focused on the accuracy of the calculated camera parameters, the reconstruction error in the computer image coordinates and in the world coordinate system and advanced image-processing techniques for subpixel detection during the comparison. The purpose of this work is to establish a basis and selection criteria for choosing one of these techniques for camera calibration, according to the accuracy required in each of the many applications using photogrammetric vision: robot calibration methods, trajectory generation algorithms, articulated measuring arm calibration, and photogrammetric systems.

2족 보행 로봇을 위한 허용 ZMP (Zero Moment Point) 영역의 활용을 통한 에너지 효율적인 기준 보행 궤적 생성

An energy-efficient reference walking trajectory generation algorithm is suggested utilizing allowable ZMP (Zero-Moment-Point) region, which maxmizes the energy efficiency for cyclic gaits, based on three-dimensional LIPM (Linear Inverted Pendulum Model) for biped robots. As observed in natural human walking, variable ZMP manipulation is suggested, in which ZMP moves within the allowable region to reduce the joint stress (i.e., rapid acceleration and deceleration of body), and hence to reduce the consumed energy. In addition, opimization of footstep planning is conducted to decide the optimal step-length and body height for a given forward mean velocity to minimize a suitable energy performance - amount of energy required to carry a unit weight a unit distance. In this planning, in order to ensure physically realizable walking trajectory, we also considered geometrical constraints, ZMP stability condition, friction constraint, and yawing moment constraint. Simulations are performed with a 12-DOF 3D biped robot model to verify the effectiveness of the proposed method.

Contour Based Path Planning with B-Spline Trajectory Generation for Unmanned Aerial Vehicles (UAVs) over Hostile Terrain

This research focuses on trajectory generation algorithms that take into account the stealthiness of autonomous UAVs; generating stealthy paths through a region laden with enemy radars. The algorithm is employed to estimate the risk cost of the navigational space and generate an optimized path based on the user-specified threshold altitude value. Thus the generated path is represented with a set of low-radar risk waypoints being the coordinates of its control points. The radar-aware path planner is then approximated using cubic B-splines by considering the least radar risk to the destination. Simulated results are presented, illustrating the potential benefits of such algorithms.

A Trajectory Generation Scheme for Precise and Safe Lunar Landing

Execution of scientific objectives such as to investigate the central peaks of a big crater of the moon is thought to be the most scientifically interesting. Precise and safe autonomous landing ability is a productive issue for this investigation. Here it is proposed a scheme of trajectory generation for lunar descent. This research includes a sketch of a qualitative scheme on solutions of motion control equations for lunar descent vehicle from orbital speed condition down to the terminal descent situation. A trajectory generation algorithm is developed accumulating more than one step with variable thrust to mass ratio. Mathematical modeling, algorithm design, simulations and results are presented in this paper. In fact, the proposed trajectory generation scheme can readily be used to develop real-time guidance algorithm for future precise and safe lunar landing missions reducing the computational burden.

1101 自律走行車両のための危険感ポテンシャルドライバモデルおよび車両運動性能を考慮した制御目標生成アルゴリズムの開発(OS3-1 自動操縦・障害物回避,OS3 交通・物流システムの制御,オーガナイズド・セッション(OS))

1101 自律走行車両のための危険感ポテンシャルドライバモデルおよび車両運動性能を考慮した制御目標生成アルゴリズムの開発(OS3-1 自動操縦・障害物回避,OS3 交通・物流システムの制御,オーガナイズド・セッション(OS))

Development of an Algorithm for the Real-time Trajectory Generation of a Control Target in a Driver Model and Vehicle Dynamics for an Autonomous Vehicle

Development of an Algorithm for the Real-time Trajectory Generation of a Control Target in a Driver Model and Vehicle Dynamics for an Autonomous Vehicle

A Novel Emergency Flight Path Planning Strategy for Civil Airplanes in Total Loss of Thrust

Emergency flight path planning process was established for the failure of total loss of thrust of both the commercial transport aircraft and the general aviation to improve the flight safety. The process of the path planning combined the landing site search and the post failure trajectory generation together. The dynamic pressure schedule was substitute for the rigid geometric preset as the restriction to ensure the smooth speed variation. Based on the variation time scales separation, the propagation logic without iteration was established for longitudinal states and commands. The top ranked landing site was selected from the approximate footprint with the radius determined by current flight states, according to the safe condition. Furthermore, a three step lateral trajectory generation algorithm can generate final trajectory and commands by linear interpolation. The trajectory can be rapidly generated for the selected landing site with satisfactory accuracy due to the incorporation of the coupling effects in flight dynamics, and the guidance commands can be tracked by basic guidance control law.

Trajectory Generation Model-Based IMM Tracking for Safe Driving in Intersection Scenario

Tracking the actions of vehicles at crossroads and planning safe trajectories will be an effective method to reduce the rate of traffic accident at intersections. It is to resolve the problem of the abrupt change because of the existence of drivers' voluntary choices. In this paper, we make approach of an improved IMM tracking method based on trajectory generation, abstracted by trajectory generation algorithm, to improve this situation. Because of the similarity between human-driving trajectory and programming trajectory which is generated by trajectory-generated algorithm, the improved IMM method performs well in tracking moving vehicles with some sudden changes of its movement. A set of data is collected for experiments when an object vehicle takes a sudden left turn in intersection scenario. To compare the experiment results between IMM method with trajectory generation model and the one without, tracking error of the former decreases by 75% in particular scenario.