Online trajectory generation using clothoid segments

Schneider, Volker; Piprek, Patrick; Schatz, Simon P.; Baier, Thaddäus; Christoph, Dorhofer; Hochstrasser, Markus; Gabrys, Agnes; Karlsson, Erik; Krause, Christoph; Lauffs, Patrick J.; Mumm, Nils C.; Kajetan, Nurnberger; Peter, Lars; Spiegel, Phillip G.; Steinert, Lukas; Zollitsch, Alexander W.; Holzapfel, Florian

doi:10.1109/icarcv.2016.7838711

Cited by 25 publications

(10 citation statements)

References 12 publications

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“…Study [7] shows some preliminary results of the trajectory generation module based on straight lines and arcs. As the direct connection of an arc and a straight line yields a curvature step, an updated version was developed by using a clothoid transition phase in [8] and enhanced kinematics for the orthogonal projection in [9]. Nevertheless, more studies must be carried out as the inevitable kink in curvature by clothoids still violates the smoothness requirement of the trajectory controller.…”

Section: Introductionmentioning

confidence: 99%

Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

et al. 2020

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In this paper, a sub-optimal trajectory optimization method is developed to generate trajectories for transition phases connecting two steady flights. Both control histories as well as the time step length that specify the trajectory for a transition maneuver are calculated as a root of an underdetermined system. Here, the unknowns are computed by a series of Newton iterations for finding the root, where explicit closed-form expressions are utilized within the algorithm to ensure computational efficiency. Moreover, a line-search strategy is incorporated to enhance the robustness. The terminal hard output constraints are guaranteed by the root finding, and the terminal control constraints are realized by using a time-varying weighting matrix in the cost function. Numerical simulations investigate multiple scenarios of transition phases, which show the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

et al. 2020

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“…The general idea of the control approach of the paper is depicted in Figure 1: The desired trajectory is generated by a suitable method, e.g., geometric approaches [15,16], (robust) optimal control [17][18][19][20], or shortest path methods [21]. As the aircraft is generally never able to follow the path exactly, either due to imperfect planning or disturbances (e.g, wind or model errors), a deviation between the aircraft reference point R and the trajectory foot point F arises.…”

Section: Introductionmentioning

confidence: 99%

“…As the aircraft is generally never able to follow the path exactly, either due to imperfect planning or disturbances (e.g, wind or model errors), a deviation between the aircraft reference point R and the trajectory foot point F arises. This point is either specified by a "virtual" aircraft that the actual aircraft "chases" (this is said to be "trajectory control" in this study) [5] or by the orthogonal projection of the aircraft reference point on the trajectory (this is said to be "path-following control" in this study), which may be calculated by the methods proposed in [15,22]. The trajectory/path-following controller then uses these deviations as well as their derivatives (velocity and acceleration) to calculate a suitable control command to reduce them.…”

Section: Introductionmentioning

confidence: 99%

Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics

et al. 2020

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This study proposes a novel, nonlinear trajectory/path-following controller based on jerk-level error dynamics. Therefore, at first the nonlinear acceleration-based kinematic equations of motion of a dynamic system are differentiated with respect to time to obtain a representation connecting the translation jerk with the (specific) force derivative. Furthermore, the path deviation, i.e., the difference between the planned and the actual path, is formulated as nonlinear error dynamics based on the jerk error. Combining the derived equations of motion with the nonlinear error dynamics as well as employing nonlinear dynamic inversion, a control law can be derived that provides force derivative commands, which may be commanded to an inner loop for trajectory control. This command ensures an increased smoothness and faster reaction time compared to traditional approaches based on a force directly. Furthermore, the nonlinear parts in the error dynamic are feedforward components that improve the general performance due to their physical connection with the real dynamics. The validity and performance of the proposed trajectory/path-following controller are shown in an aircraft-related application example.

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“…Besides, these trajectories are useful to avoid the abrupt change of the curvature that causes trouble like a slip. Because of these reasons, such trajectories are often used in trajectory planning [8]- [10]. D.H. Shin et al proposed a method of generating a path using clothoid segments [11].…”

Section: Introductionmentioning

confidence: 99%

On the Method of Generating a Circular-Clothoid Trajectory for Front-Steering Vehicles Based on L1/L2-Optimal Control

Hamada

Maruta

Fujimoto

et al. 2020

SICE Journal of Control, Measurement, and System Integration

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The continuity and the constantness of both the curvature and the velocity in a trajectory are essential for the vehicle trajectory design from the viewpoint of the followability. This paper presents a new method of generating a vehicle trajectory whose curvature and velocity continuously change while both are constant in large part. The generated trajectory is called a circular-clothoid trajectory defined as the trajectory connecting circular curves with clothoid curves. In the method, the trajectory generation problem is formulated as an L 1 /L 2-optimal control problem for front-steering vehicles. The desired trajectory is obtained numerically by solving a two-point boundary value problem that is relevant to the optimal control problem. The effectiveness of the proposed method is confirmed through some examples.

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Online trajectory generation using clothoid segments

Cited by 25 publications

References 12 publications

Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics

On the Method of Generating a Circular-Clothoid Trajectory for Front-Steering Vehicles Based on L1/L2-Optimal Control

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