Trajectory Generation Approach Research Articles

Problem of Cost Function Synthesis for Mobile Robot’s Trajectory and the Network Operator Method for its Solution

In mobile robotic systems are designed for patrolling and protecting large areas, in difficult conditions, when environmental constraints severely limit the space of acceptable motions preferences, a state space sampling strategy is more effective, than sampling in the space of controls. Although this has been evident for some time, the practical question is how to achieve it while also satisfying the severe constraints of vehicle dynamic feasibility. The paper presents a new the network operator method for state space sampling utilizing a model-based trajectory generation approach

Reference Trajectories for Investigating Fault-Tolerant Trajectory Tracking Control Algorithms for Automated Vehicles

Abstract The automation of road vehicles implies highest demands for all parts involved in the driving task, including the vehicle actuators. Fault-tolerant trajectory tracking, which exploits functional redundancies among the vehicle actuators, bears the potential to avoid fail-operational requirements on actuator level. Yet, the use of fault-tolerant trajectory tracking must be well argued as the number of possible driving scenarios of automated vehicles is virtually unlimited. We present a reference trajectory generation approach in order to support such a safety argumentation. The generation essentially respects functional limits of the specific vehicle automation application, e.g., maximum speed or lateral acceleration. Derived from standard maneuvers of automated vehicles, the trajectories are generated with varying paths and speed profiles for the specific application. Eventually, a set of trajectories is generated for an example application and applied to investigate the potential of a selected fault-tolerant trajectory tracking approach. The simulation results for the example application reveal the shortcomings of the selected fault-tolerant trajectory tracking algorithm. However, these results also indicate that fault-tolerant trajectory tracking can be employed within the example application once the shortcomings of the algorithm are resolved.

Convex Properties of Center-of-Mass Trajectories for Locomotion Based on Divergent Component of Motion

This letter presents an in-depth analysis of the convex properties of center-of-mass (CoM) trajectories for legged robot locomotion based on the concept of Divergent Component of Motion (DCM). In particular, we show that the union of all possible trajectories forms a bounded convex set under appropriate boundary conditions. Additionally, we describe in detail our approach of generating closed-form CoM trajectories through piecewise interpolation over a sequence of waypoints and show how to compute the CoM trajectory efficiently through equations given in a matrix form. Applying the convex properties to our trajectory-generation approach, we present an algorithm for computing convex overapproximations of the CoM waypoints. Finally, we provide an example of usage in placing waypoints that lead to feasible CoM trajectories with respect to kinematic and dynamic constraints. The approach is validated with a multi-contact scenario in simulation with the humanoid robot TORO.

Clothoid-Augmented Online Trajectory Generation for Radius to Fix Turns

A trajectory generation approach for the radius to fix leg type is presented, which uses clothoids to ensure smooth transitions between straight and circular sections of the flight path. The derived algorithm is implemented in an integrated modular mission management system for manned and unmanned aerial systems. The trajectory generation module generates inputs for a nonlinear dynamic inversion based 3D trajectory controller using second order error dynamics. By using clothoid segments at the turn-in and turnout transitions, continuous curvature paths can be computed. The capability of the proposed method is demonstrated in flight with a CS-23 experimental aircraft.

A Robot Trajectory Optimization Approach for Thermal Barrier Coatings Used for Free-Form Components

This paper is concerned with a robot trajectory optimization approach for thermal barrier coatings. As the requirements of high reproducibility of complex workpieces increase, an optimal thermal spraying trajectory should not only guarantee an accurate control of spray parameters defined by users (e.g., scanning speed, spray distance, scanning step, etc.) to achieve coating thickness homogeneity but also help to homogenize the heat transfer distribution on the coating surface. A mesh-based trajectory generation approach is introduced in this work to generate path curves on a free-form component. Then, two types of meander trajectories are generated by performing a different connection method. Additionally, this paper presents a research approach for introducing the heat transfer analysis into the trajectory planning process. Combining heat transfer analysis with trajectory planning overcomes the defects of traditional trajectory planning methods (e.g., local over-heating), which helps form the uniform temperature field by optimizing the time sequence of path curves. The influence of two different robot trajectories on the process of heat transfer is estimated by coupled FEM models which demonstrates the effectiveness of the presented optimization approach.

Trajectory generation of heat load test based on gauss pseudospectral method

A new trajectory generation for heat load test is proposed based on gauss pseudospectral method within limit range. Firstly, with multiple path constraints and flight task requirements taken into consideration, heat load parameters are introduced into the dynamics equations. In order to solve the problem of generating such a trajectory within limit range rapidly, the dynamics equations have been normalized by Earth related parameters. Secondly, since the gauss pseudospectral method is just employed to solve the discrete nonlinear programming problem, transformations are developed, which can relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. In addtion, another approach of trajectory generation by tracking the given heat rate is also presented. Finally, simulation results with common aero vehicle (CAV-H) show that the trajectories obtained by both methods can well perform the heat load test with high stagnation heating rate and the large total aeroheating amount; meanwhile, gauss pseudospectral method is better than the compared one in the given range. Furthermore, the 3-D trajectory states and control variables, angle of attack and bank, which are generated by gauss pseudospectral method, can change smoothly.

Reentry trajectory optimization with waypoint and no-fly zone constraints using multiphase convex programming

This study proposes a multiphase convex programming approach for rapid reentry trajectory generation that satisfies path, waypoint and no-fly zone (NFZ) constraints on Common Aerial Vehicles (CAVs). Because the time when the vehicle reaches the waypoint is unknown, the trajectory of the vehicle is divided into several phases according to the prescribed waypoints, rendering a multiphase optimization problem with free final time. Due to the requirement of rapidity, the minimum flight time of each phase index is preferred over other indices in this research. The sequential linearization is used to approximate the nonlinear dynamics of the vehicle as well as the nonlinear concave path constraints on the heat rate, dynamic pressure, and normal load; meanwhile, the convexification techniques are proposed to relax the concave constraints on control variables. Next, the original multiphase optimization problem is reformulated as a standard second-order convex programming problem. Theoretical analysis is conducted to show that the original problem and the converted problem have the same solution. Numerical results are presented to demonstrate that the proposed approach is efficient and effective.

An Efficient Approach of Time-Optimal Trajectory Generation for the Fully Autonomous Navigation of the Quadrotor

In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V≈1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: Vmax=1 m/s, Amax=2 m/s2, and Jmax=5 m/s3. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

Trajectory Generation for Unmanned Aerial Manipulators Through Quadratic Programming

In this paper, a trajectory generation approach using quadratic programming is described for aerial manipulation, i.e. , for the control of an aerial vehicle equipped with a robot arm. The proposed approach applies the online active set strategy to generate a feasible trajectory of the joints, in order to accomplish a set of tasks with defined bounds and constraint inequalities. The definition of the problem in the acceleration domain allows to integrate and perform a large set of tasks and, as a result, to obtain smooth motion of the joints. A weighting strategy, associated with a normalization procedure, allows us to easily define the relative importance of the tasks. This approach is useful to accomplish different phases of a mission with different redundancy resolution strategies. The performance of the proposed technique is demonstrated through real experiments with all the algorithms running onboard in real time. In particular, the aerial manipulator can successfully perform navigation and interaction phases, while keeping motion within prescribed bounds and avoiding collisions with external obstacles.

Optimisation of Reference Gait Trajectory of a Lower Limb Exoskeleton

Lower limb exoskeletons have gained considerable interest in recent years as a research topic for creating aids for people with walking disabilities and strength augmenters for pilot walkers. A crucial practical problem, however, is generating the reference trajectory of the joints. In this paper, we solve the reference trajectory problem by a novel approach which obtains the angle trajectories of knee joints from the hip joints. The relationship between the angle trajectories of the knee and hip joints is acquired through kinematic models of the lower limb exoskeleton. In these models, the parameters of the joint position trajectories are optimised by a swarm fish algorithm with variable population. The proposed approach is validated in virtual simulations and a physical prototype of an exoskeleton system. The experimental results confirm that the reference trajectory generation approach accurately reproduces human walking.

Entry trajectory planning based on three-dimensional acceleration profile guidance

A new entry trajectory generation approach based on rapid planning three-dimensional acceleration profile (TDAP) is proposed in this paper. The TDAP planner concept means extending the traditional drag planning approach into three dimensional drag space to accommodate much larger downrange or cross-range, and improve the maneuvering capability by utilizing both angle of attack and bank as primary control commands. To figure out this problem, firstly, the planner transforms the generation of TDAP into scheming two sub-profiles, longitudinal drag acceleration profile and lateral lift to drag acceleration profile in parallel. Each profile is generated in the corridor converted by all path constraints correspondingly. Secondly, a reduced order dynamics system is employed to extract all standard state variables and adjust the three-dimensional acceleration profile, ensuring the terminal position precision requirement to be met. Finally, a combined proportional derivative (PD) feedback law is designed to track the reference profile. Simulations with the Common Aero Vehicle (CAV) model show that the 3-D trajectories of both planned and generated by the guidance law can successfully satisfy all path constraints and flight task requirements.

Vision-based landing site evaluation and informed optimal trajectory generation toward autonomous rooftop landing

Autonomous landing is an essential function for micro air vehicles (MAVs) for many scenarios. We pursue an active perception strategy that enables MAVs with limited onboard sensing and processing capabilities to concurrently assess feasible rooftop landing sites with a vision-based perception system while generating trajectories that balance continued landing site assessment and the requirement to provide visual monitoring of an interest point. The contributions of the work are twofold: (1) a perception system that employs a dense motion stereo approach that determines the 3D model of the captured scene without the need of geo-referenced images, scene geometry constraints, or external navigation aids; and (2) an online trajectory generation approach that balances the need to concurrently explore available rooftop vantages of an interest point while ensuring confidence in the landing site suitability by considering the impact of landing site uncertainty as assessed by the perception system. Simulation and experimental evaluation of the performance of the perception and trajectory generation methodologies are analyzed independently and jointly in order to establish the efficacy and robustness of the proposed approach.

Incremental approach for trajectory generation of spray painting robot

Purpose This paper aims to present a new offline robot programming approach for automated trajectory generation on free-form surfaces targeted toward spray painting application. Design/methodology/approach In this paper, an incremental trajectory generation approach is developed where new paint passes are generated based on paint deposited on the surface as a result of previous paint passes. The trajectory is generated on real surfaces where optimal velocity is calculated using genetic algorithm considering parameters such as surface model, spray gun model, paint distribution model and task constraints. Findings The developed approach was implemented on various surfaces for different paint distribution patterns, and the simulation results reveal that the approach is flexible and efficient to handle variety in part geometry and paint distribution. From experimental validation and analysis of results thus obtained, the developed approach is highly promising compared to the existing methods. Research limitations/implications The approach assumes that the computer-aided design (CAD) model of the surface is available and is limited to surjective surfaces in a structured environment where the spray gun characteristics and process parameters are known beforehand. Practical implications The problem of programming a robot manually is overcome by automatically generating a sub-optimal trajectory which can be easily transferred to an industrial robot for spray painting the surface. Originality/value This paper discusses a new approach for automated trajectory generation from CAD model. The experimental validation of the developed approach is successfully performed on a highly curved test surface, and obtained results are in agreement with the simulation results.

Novel integrated offline trajectory generation approach for robot assisted spray painting operation

In this paper a novel integrated offline programming methodology for automated robot trajectory generation on free form surfaces is developed. Based on the computer-aided design model of a part, the tool model, task constraints and optimization criteria the trajectory is generated in an integrated manner. The proposed approach focuses on discretizing a surface into several ‘sections’ and simultaneous trajectory generation for the robot considering the local geometrical behavior of the surface and its effect globally. This research is primarily targeted toward generation of robot trajectory to spray paint a free form surface with desired paint thickness and minimum paint thickness deviation in a structured environment. The proposed approach was implemented on automobile parts to determine the effectiveness and robustness of designed algorithm. The simulation results and experimental validation on test surfaces revealed that the approach is flexible and efficient to handle variety in part geometry and the paint distribution.

Development of a Quadrotor Test Bed — Modelling, Parameter Identification, Controller Design and Trajectory Generation

In this paper, a quadrotor test bed is developed. The technical approach for this test bed is firstly proposed by utilizing a commercial quadrotor, a Vicon motion capture system and a ground station. Then, the mathematical model of the quadrotor is formulated considering aerodynamic effects, and the parameter identification approaches for this model are provided accordingly. Based on the developed model and identified parameters, a simulation environment that is consistent with the real system is developed. Subsequently, a flight control strategy and a trajectory generation method, both of which are conceptually and computationally lightweight, are developed and tested in the simulation environment. The developed algorithms are then directly transplanted to the real system, and the experimental results show that their responses in the real-time flights match well with those from the simulations. This indicates that the control algorithms developed for the quadrotor can be preliminarily verified and refined though simulations, and then directly implemented to the real system, which could significantly reduce the experimental risks and costs. Meanwhile, real-time experiments show that the developed flight controller can efficiently stabilize the quadrotor when external disturbances exist, and the trajectory generation approach can provide safe guidance for the quadrotor to fly smoothly through cluttered environments with obstacle rings. All of these features are valuable for real applications, thus demonstrating the feasibility of further development.

Damaged Airplane Trajectory Planning Based on Flight Envelope and Motion Primitives

This paper presents an efficient approach for safe landing trajectory generation of an airplane with structural damage to its wing flying in proximity to local terrain. A damaged airplane maneuvering flight envelope is estimated by analyzing the local stability and flying quality at each trim condition. Trim state distance to a flight envelope boundary provides a novel criterion defined as the safety value index to prioritize choice of trim conditions for postdamage flight. A library of trajectory segments including trim states and transition maneuvers between trim conditions in the local neighborhood are generated using a linear quadratic regulator controller. A potential field strategy is used to rapidly define emergency landing trajectories composed as trim state sequences based on criteria including terrain avoidance, safety value index, and safe landing requirements such as touchdown heading and position, airspeed, glide slope, and bank angle. Cost criteria are balanced by adjusting weights. Landing scenarios are presented to demonstrate the capability of the proposed approach to autonomously plan safe landing trajectories.

Bioinspired 4D Trajectory Generation for a UAS Rapid Point-to-Point Movement

A bioinspired trajectory generation approach for Unmanned Aerial System (UAS) rapid Point-to-Point (PTP) movement was presented. The approach was based on general tau theory developed by biologists from observing and studying the behavior of birds and some other animals. We applied the bioinspired approach to the rapid PTP movement problem of a rotary UAS and derived two different trajectory planning strategies, namely, the tau coupling strategy and the intrinsic tau gravity guidance strategy. Based on general tau theory, according to the dynamic model of UAS, we presented a new strategy named intrinsic tau jerk guidance which can fit the movement that the initial acceleration of the UAS is zero. With new strategies, flight trajectory generation examples with a UAS were presented. The kinematics and dynamics analyses of the UAS for rapid PTP movement were presented with simulation results which show that the generated trajectories were feasible.

Generating a Style-Adaptive Trajectory from Multiple Demonstrations

Trajectory learning and generation from demonstration have been widely discussed in recent years, with promising progress made. Existing approaches, including the Gaussian Mixture Model (GMM), affine functions and Dynamic Movement Primitives (DMPs) have proven their applicability to learning the features and styles of existing trajectories and generating similar trajectories that can adapt to different dynamic situations. However, in many applications, such as grasping an object, shooting a ball, etc., different goals require trajectories of different styles. An issue that must be resolved is how to reproduce a trajectory with a suitable style. In this paper, we propose a style-adaptive trajectory generation approach based on DMPs, by which the style of the reproduced trajectories can change smoothly as the new goal changes. The proposed approach first adopts a Point Distribution Model (PDM) to get the principal trajectories for different styles, then learns the model of each principal trajectory independently using DMPs, and finally adapts the parameters of the trajectory model smoothly according to the new goal using an adaptive goal-to-style mechanism. This paper further discusses the application of the approach on small-sized robots for an adaptive shooting task and on a humanoid robot arm to generate motions for table tennis-playing with different styles.

Curvature-constrained trajectory generation for waypoint following for miniature air vehicle

This paper addresses trajectory generation problem of a fixed-wing miniature air vehicle, constrained by bounded turn rate, to follow a given sequence of waypoints. An extremal path, named as γ-trajectory, that transitions between two consecutive waypoint segments (obtained by joining two waypoints in sequence) in a time-optimal fashion is obtained. This algorithm is also used to track the maximum portion of waypoint segments with the desired shortest distance between the trajectory and the associated waypoint. Subsequently, the proposed trajectory is compared with the existing transition trajectory in the literature to show better performance in several aspects. Another optimal path, named as loop trajectory, is developed for the purpose of tracking the waypoints as well as the entire waypoint segments. This paper also proposes algorithms to generate trajectories in the presence of steady wind to meet the same objective as that of no-wind case. Due to low computational burden and simplicity in the design procedure, these trajectory generation approaches are implementable in real time for miniature air vehicles.

Rapid generation of entry trajectories with waypoint and no-fly zone constraints

Waypoints are positions for multiple payload deployments or reconnaissance missions, and no-fly zones are exclusion zones that cannot be passed for threat avoidance or due to geopolitical restrictions. This paper proposes a rapid entry trajectory generation approach satisfying waypoint and no-fly zone constraints for entry vehicles with relatively high lift-to-drag ratio. A lateral planning algorithm based on a Newton iteration scheme is developed to simultaneously design both the magnitude and sign of the control variable according to waypoints and no-fly zones. The algorithm converts the highly constrained trajectory planning problem into a series of one-parameter search problems based on a reduced-order system. Then, the quasi-equilibrium glide phenomenon is employed to extract the remaining state variables corresponding to longitudinal motion. The algorithm is tested using the Common Aero Vehicle model, and the results demonstrate that the algorithm can generate flyable entry trajectories rapidly within allowable tolerances while satisfying all the flight constraints.