Trajectory Generation Method Research Articles

Onboard trajectory generation for gyroplane unpowered landing based on optimal lift-to-drag ratio target

To achieve the autonomous unpowered landing for gyroplanes, an onboard trajectory generation method is presented in this paper. As a pivotal variable in the proposed method, the Lift-to-Drag Ratio will be uniquely determined in different phases by finding the maximum for the energy margin during approaching and the energy decrease at terminal landing. Especially, autorotation constraint, the primary requirement of gyroplanes for flight stability, has been considered as a limitation factor through this procedure. Furthermore, a geometrically constrained three-dimensional trajectory profile is employed, in which a multi-circle Heading Align Cone is proposed to improve its applicability. Accordingly, a predictor–corrector algorithm is derived and described for trajectory generation with initial variance and terminal requirements. Employing the algorithm onboard, by adjusting few geometric parameters dynamically, a feasible trajectory reference that meets the specified constraints can be generated efficiently. Results from numerical calculation and closed-loop simulation under different scenarios demonstrate the effectiveness and robustness of the approach.

Trajectory optimization and state selection for urban automated driving

The automated driving is an emerging technology in which a car performs recognition, decision making, and control. The decision-making system consists of route planning and trajectory planning. The route planning optimizes the shortest path to the destination like an automotive navigation system. According to static and dynamic obstacles around the vehicle, the trajectory planning generates lateral and longitudinal profiles for vehicle maneuver to drive the given path. This study is focused on the trajectory planning for vehicle maneuver in urban traffic scenes. This paper proposes a trajectory generation method that extends the existing method to generate more natural behavior with small acceleration and deceleration. This paper introduces an intermediate behavior to gradually switch from the velocity keeping to the distance keeping. The proposed method can generate smooth trajectory with small acceleration/deceleration. Numerical experiments show that the vehicle generates smooth behaviors according to surrounding vehicles.

Real-Time Trajectory Generation for Haptic Feedback Manipulators in Virtual Cockpit Systems

To obtain real-time interactions in the virtual cockpit system (VCS), a real-time trajectory generation method based on dynamical nonlinear optimization and regression prediction for the haptic feedback manipulator (HFM) is presented in this paper. First, a haptic feedback system based on servoserial manipulator is constructed. Then, the trajectory planning problem for the HFM is formulated as a nonlinear optimization problem to balance the motion time and power consumption and ensure the safety of physical human–robot interactions (pHRI). Multiple optimization problems are solved to generate the optimal database off-line. Finally, the classified multivariate (CM) regression method is presented to learn the database and generate optimal trajectories with arbitrary initial and objective positions on-line. Results show that trajectories with rapidity, safety, and lower power consumption can be generated in real-time by this method, which lay a basis of haptic interactions in the VCS.

A learning framework for semantic reach-to-grasp tasks integrating machine learning and optimization

The ability to implement semantic Reach-to-grasp (RTG) tasks successfully is a crucial skill for robots. Given unknown objects in an unstructured environment, finding an feasible grasp configuration and generating a constraint-satisfied trajectory to reach it are challenging. In this paper, a learning framework which combines semantic grasp planning with trajectory generation is presented to implement semantic RTG tasks. Firstly, the object of interest is detected by using an object detection model trained by deep learning. A Bayesian-based search algorithm is proposed to find the grasp configuration with highest probability of success from the segmented image of the object using a trained quality network. Secondly, for robotic reaching movements, a model-based trajectory generation method inspired by the human internal model theory is designed to generate a constraint-satisfied trajectory. Finally, the presented framework is validated both in comparative analysis and on real-world experiments. Experimental results demonstrated that the proposed learning framework enables the robots to implement semantic RTG tasks in unstructured environments.

Enabling Driving Cycle Loss Reduction in Variable Flux PMSMs Via Closed-Loop Magnetization State Control

Variable flux permanent magnet synchronous machines (VF-PMSMs) have recently been proposed to reduce driving cycle losses in electric vehicle traction motors via magnetization state (MS) manipulation. This paper presents a closed-loop MS control method to enable reliable loss minimization control of VF-PMSMs. The MS is estimated at every sample instant and is used as a feedback for closed-loop control. Under most circumstances, the proposed method maintains precise torque control even during the MS manipulation transient by using a deadbeat-direct torque and flux control (DB-DTFC) framework. The state-of-the-art high-speed flux trajectory generation method for MS manipulation is integrated in the new closed-loop method to allow MS manipulation up to the maximum speed within the inverter voltage limit. The effectiveness of the proposed methods, in terms of driving cycle loss reduction capability and its thermal impact, is evaluated experimentally by emulating the road load using the dynamometer load motor.

A Driving Behavior Planning and Trajectory Generation Method for Autonomous Electric Bus

A framework of path planning for autonomous electric bus is presented. ArcGIS platform is utilized for map-building and global path planning. Firstly, a high-precision map is built based on GPS in ArcGIS for global planning. Then the global optimal path is obtained by network analysis tool in ArcGIS. To facilitate local planning, WGS-84 coordinates in the map are converted to local coordinates. Secondly, a double-layer finite state machine (FSM) is devised to plan driving behavior under different driving scenarios, such as structured driving, lane changing, turning, and so on. Besides, local optimal trajectory is generated by cubic polynomial, which takes full account of the safety and kinetics of the electric bus. Finally, the simulation results show that the framework is reliable and feasible for driving behavior planning and trajectory generation. Furthermore, its validity is proven with an autonomous bus platform 12 m in length.

Real-Time Trajectory Generation Methods for Cooperating Mobile Manipulators Subject to State and Control Constraints

This paper deals with the real-time trajectory generation problem for two cooperating mobile robots moving the common rigid object. The holonomic constraints resulting from a closed kinematic chain and the dynamics of such a system are considered. Two methods of generation sub-optimal trajectories allowing for mechanical and control limitations and collision avoidance conditions are proposed. The first solution is based on a leader-follower approach, in the second one the robotic system is treated as a whole mechanism. In both cases, the trajectories are generated in order to avoid singularities and they are scaled to satisfy control constraints. Advantages and disadvantages of both presented approaches are discussed. A computer example involving two mobile manipulators consisting of nonholonomic platform (2,0) class and planar 3-DOF holonomic manipulator is presented.

Covering Method for Trajectory Generation and Orbital Decomposition of Systems

Based on previously stated approaches, we propose a method for solving point-topoint steering problems in the case where a 2n-parametric family of solutions of a nonlinear system is known and for Liouville systems. Two examples of the helicopter motions in the vertical plane and the Kapitsa pendulum are considered to demonstrate the efficiency of the proposed method.

A three-stage trajectory generation method for robot-assisted bilateral upper limb training with subject-specific adaptation

Robot-assisted bilateral upper limb training typically requires two robotic devices that work cooperatively with a human user. The determination of appropriate movement trajectories is essential to avoid interference of the robotic systems and ensure an appropriate intersecting workspace with user limbs. This paper proposes a new three-stage trajectory generation method for bilateral upper limb training using interference analysis. These three stages include workspace analysis of robots and human hands, trajectory generation within the intersecting workspace, and interference analysis for training safety verification. This trajectory generation method is also implemented with subject-specific adaptation based on anthropometry of an individual. Experiments were conducted on seven healthy subjects with a variety of body sizes. All participants gave positive feedback on the suitability of the predefined training trajectories, and no robot interference was detected. This three-stage method provides guidelines for the standardization of robot-assisted bilateral upper limb training protocols. Future work will focus on proposing an adaptive trajectory generation algorithm with efficacy evaluation on a larger sample of subjects.

Collision-Free Trajectory Generation and Tracking for UAVs Using Markov Decision Process in a Cluttered Environment

A collision-free trajectory generation and tracking method capable of re-planning unmanned aerial vehicle (UAV) trajectories can increase flight safety and decrease the possibility of mission failures. In this paper, a Markov decision process (MDP) based algorithm combined with backtracking method is presented to create a safe trajectory in the case of hostile environments. Subsequently, a differential flatness method is adopted to smooth the profile of the rerouted trajectory for satisfying the UAV physical constraints. Lastly, a flight controller based on passivity-based control (PBC) is designed to maintain UAV’s stability and trajectory tracking performance. Simulation results demonstrate that the UAV with the proposed strategy is capable of avoiding obstacles in a hostile environment.

Dynamic modeling and CPG-based trajectory generation for a masticatory rehab robot

Human mastication is a complex and rhythmic biomechanical process which is regulated by a brain stem central pattern generator (CPG). Masticatory patterns, frequency and amplitude of mastication are different from person to person and significantly depend on food properties. The central nervous system controls the activity of muscles to produce smooth transitions between different movements. Therefore, to rehab human mandibular system, there is a real need to use the concept of CPG for development of a new methodology in jaw exercises and to help jaw movements recovery. This paper proposes a novel method for real-time trajectory generation of a mastication rehab robot. The proposed method combines several methods and concepts including kinematics, dynamics, trajectory generation and CPG. The purpose of this article is to provide a methodology to enable physiotherapists to perform the human jaw rehabilitation. In this paper, the robotic setup includes two Gough–Stewart platforms. The first platform is used as the rehab robot, while the second one is used to model the human jaw system. Once the modeling is completed, the second robot will be replaced by an actual patient for the selected physiotherapy. Gibbs–Appell’s formulation is used to obtain the dynamics equations of the rehab robot. Then, a method based on the Fourier series is employed to tune parameters of the CPG. It is shown that changes in leg lengths, due to the online changes of the mastication parameters, occur in a smooth and continuous manner. The key feature of the proposed method, when applied to human mastication, is its ability to adapt to the environment and change the chewing pattern in real-time parameters, such as amplitudes as well as jaw movements velocity during mastication.

An Acquisition of Trajectory Generation Method for Tool Operation Based on MITATE from Human Demonstration

An Acquisition of Trajectory Generation Method for Tool Operation Based on MITATE from Human Demonstration

Including Linear Holding in Air Traffic Flow Management for Flexible Delay Handling

This paper introduces a strategy to include linear holding into air traffic flow management initiatives, together with the commonly used ground holding and airborne holding measures. In this way, flow management performance can be improved when handling delay assignment with uncertainty. First, a trajectory generation method is presented, aiming at computing, per flight, the maximum linear holding realizable using the same fuel as the original nominal flight. This information is assumed to be computed and shared by the different airlines and it is then used to build a network air traffic flow management model to optimally assign delays, in the scope of trajectory-based operations. Hence, the best distribution of delay is optimized at given positions along the flight trajectory (combining the three holding practices together) and taking into account the cost of delay, especially in the fuel consumption. The problem is formulated as a mixed integer linear program and solved with a commercial off-the-shelf solver. An illustrative example is given, showing that under the circumstance of capacity recovered ahead of schedule, including linear holding contributes to a notable delay reduction compared with the case where only ground and airborne holding apply.

Real-Time Motion Planning for Aerial Videography With Dynamic Obstacle Avoidance and Viewpoint Optimization

We propose a method for real-time trajectory generation with applications in aerial videography. Taking framing objectives, such as position of targets in the image plane, as input, our method solves for robot trajectories and gimbal controls automatically and adapts plans in real time due to changes in the environment. We contribute a real-time receding horizon planner that autonomously records scenes with moving targets, while optimizing for visibility under occlusion and ensuring collision-free trajectories. A modular cost function, based on the reprojection error of targets, is proposed that allows for flexibility and artistic freedom and is well behaved under numerical optimization. We formulate the minimization problem under constraints as a finite horizon optimal control problem that fulfills aesthetic objectives, adheres to nonlinear model constraints of the filming robot and collision constraints with static and dynamic obstacles and can be solved in real time. We demonstrate the robustness and efficiency of the method with a number of challenging shots filmed in dynamic environments including those with moving obstacles and shots with multiple targets to be filmed simultaneously.

A simultaneous trajectory generation method for quadcopter intercepting ground mobile vehicle

This article proposes a trajectory generator for quadcopter to intercept moving ground vehicle. For this air–ground interaction problem, we formulate the trajectory generation problem as quadratic dynamic programming in a moving-horizon scheme based on the quadcopter kinematics and observation to ground vehicle. The closed-form solution of quadratic dynamic programming in each iteration enables this algorithm a real-time replanning performance. Thereafter, segmented trajectory rule, inspired from commercial flight landing regular, is implemented to guarantee smoothness in approaching and interception to moving ground target from comparably far origin. Our established algorithm is verified through both simulations and experiments.

Smooth Sub-Phases Based Trajectory Planning for Exoskeleton System

Trajectory is a crucial part of exoskeleton robot design. The appropriate trajectory will affect wearer's safety, health and comfort. The trajectory profile of angular position can be generated as same as actual trajectory profile in term of shape. However, the problem of unreachable intermediate points increases the error between the polynomial trajectory profile and real human trajectory profile. This error directly can affect to generate a less accurate profile that can’t be accurately matched to the human trajectory profile. Based on the aforementioned problem, the objectives of this paper is to investigate the effect of having a different number of sub-phases trajectories on the error related to the real human trajectory profile. Also, this paper presents trajectory generation method that is called quintic polynomial segment with 6th polynomial blend (6-5-6 PSPB). The 6-5-6 PSPB trajectory includes the via points at initial and final of each phase in order to solve the problem of unreachable intermediate points. The result shows a good improvement (almost 8%) in term of error based on the proposed 6-5-6 PSPB technique compared to the three categories of gait analysis. The 6-5-6 PSPB technique shows a good result based on the root mean square error (RMSE) and average difference (AD) error of angular position (0.3146 and 0.031310 Degree respectively). At the end, 6-5-6 PSPB can improve the error and generate a trajectory motion profile that accurately matches to human trajectory profile.

Stochastic Trajectory Generation Using Particle Swarm Optimization for Quadrotor Unmanned Aerial Vehicles (UAVs)

The aim of this paper is to provide a realistic stochastic trajectory generation method for unmanned aerial vehicles that offers a tool for the emulation of trajectories in typical flight scenarios. Three scenarios are defined in this paper. The trajectories for these scenarios are implemented with quintic B-splines that grant smoothness in the second-order derivatives of Euler angles and accelerations. In order to tune the parameters of the quintic B-spline in the search space, a multi-objective optimization method called particle swarm optimization (PSO) is used. The proposed technique satisfies the constraints imposed by the configuration of the unmanned aerial vehicle (UAV). Further particular constraints can be introduced such as: obstacle avoidance, speed limitation, and actuator torque limitations due to the practical feasibility of the trajectories. Finally, the standard rapidly-exploring random tree (RRT*) algorithm, the standard (A*) algorithm and the genetic algorithm (GA) are simulated to make a comparison with the proposed algorithm in terms of execution time and effectiveness in finding the minimum length trajectory.

Ascent guidance for air-breathing hypersonic vehicles based on dynamic inversion

This article presents an adaptive ascent guidance strategy based on dynamic inversion for air-breathing hypersonic vehicles. Since dynamic inversion is effective to deal with nonlinear problems, this method is employed here to design the ascent guidance command. Compared with conventional dynamic inversion, an adaptive scheme is added into the guidance strategy, which significantly improves the robust performance of this method. And the stability analysis is given to prove the convergence of the nonlinear system. Besides, considering the real-world dynamic motions of the vehicle should be aware to calculate the guidance command instead of referring to the nominal model, the least squares algorithm with forgetting factor is adopted in this article to estimate the real thrust acceleration. And the reference trajectory generated online by polynomial fitting shows better adaptation to the change of flight environment and less computation time than other trajectory generation methods. Results of simulation are provided to demonstrate the feasibility and effectiveness of this approach.

Path smoothing for five-axis machine tools using dual quaternion approximation with dominant points

Nowadays, G01 blocks are still the most widely utilized representation form for the tool paths in the five-axis machine tools. Tangency and curvature discontinuities of the linear tool paths may lead to frequent feedrate fluctuation and acceleration variation, which inevitably deteriorate the machining efficiency and quality. To solve this problem, this paper proposed a dual quaternion B-spline approximation method of dominant points to generate smooth tool paths for five-axis CNC machine tools. First, the dominant points, which can characterize the shape of the linear path, are selected for the tool tip location and the tool orientation simultaneously. Such scheme can significantly compress the number of the control points and release the computational load. Then, the linear tool paths are converted to dual quaternions and approximated to dual quaternion B-spline, which can realize the parameter synchronization for the tool tip and tool orientation, and avoid the fitting oscillatory as well. To verify the proposed method, a trajectory generation method for the dual quaternion B-spline is developed. Simulations and experiments on a five-axis machine tool are conducted, and the results demonstrate the feasibility and efficiency of the proposed method.

Generation of movements with boundary conditions based on optimal control theory

Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control theory and is based on a second order dynamic system. We evaluate our method and compare it to the state of the art movement generation methods in both simulations and real robot experiments. We show that the new method is very compact in its representation and can reproduce reference trajectories with zero error. Moreover, it has most of the features of the state of the art movement generation methods such as robustness to perturbations and generalization to new position and velocity boundary conditions. We believe that, due to these features, our method may have potential for robotic applications where high accuracy is required paired with flexibility, for example, in modern industrial robotic applications, where more flexibility will be demanded as well as in medical robotics.