Enhanced Kinematics Calculation for an Online Trajectory Generation Module

Piprek, Patrick; Schneider, Volker; Fafard, Vincent; Schatz, Simon P.; Christoph, Dorhofer; Lauffs, Patrick J.; Peter, Lars; Holzapfel, Florian

doi:10.1016/j.trpro.2018.02.028

Cited by 5 publications

(7 citation statements)

References 10 publications

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“…This is the speed with which the maneuvers are planned. Looking at Equation (34), it is clear that the speed is proportional to the maneuver radius r c . Therefore, the higher the speed, the bigger the maneuver circle will be.…”

Section: Implementation Considerationsmentioning

confidence: 99%

“…As we stated before, our goal is to have a clothoid section that starts with a curvature κ = 0 and ends with a curvature κ = 1 r c , which is the curvature of the maneuver circle calculated by Equation (34). This means that we want the curvature of the clothoid, which we can parametrize with Equation ( 26), to equal 1 r c :…”

mentioning

confidence: 99%

“…where µ cmd and r c are calculated using Equation (33) and Equation (34), respectively. Equation (41) gives us a parametrization of the clothoid shaping parameter A as a function of the aircraft dynamics and performance.…”

mentioning

confidence: 99%

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Online Deterministic 3D Trajectory Generation for Electric Vertical Take-Off and Landing Aircraft

Mbikayi,

Steinert,

Heimsch

et al. 2024

Aerospace

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The use of non-piloted eVTOL aircraft in non-segregated airspace requires reliable and deterministic automatic flight guidance systems for the aircraft to remain predictable to all the users of the airspace and maintain a high level of safety. In this paper we present a 3D trajectory generation module based on clothoid transition segments in the horizontal plane and high order polynomial transition segments in the vertical plane. The expressions of the coefficients of the polynomial are derived offline are used to generate the trajectory online, making the system capable of running in real time without requiring enormous computational power. For the horizontal plane, we focus on the flyby transition, and therefore present a thorough analysis of the flyby geometry and the limitations linked to this geometry and the construct of three-segment trajectory generation around a fixed turn rate. We present feasible solutions for these limitations, and show simulation results for the combined horizontal and vertical plane concepts, allowing the system to generate complex 3D trajectories.

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Section: Implementation Considerationsmentioning

confidence: 99%

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confidence: 99%

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Online Deterministic 3D Trajectory Generation for Electric Vertical Take-Off and Landing Aircraft

Mbikayi,

Steinert,

Heimsch

et al. 2024

Aerospace

Self Cite

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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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“…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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Enhanced Kinematics Calculation for an Online Trajectory Generation Module

Cited by 5 publications

References 10 publications

Online Deterministic 3D Trajectory Generation for Electric Vertical Take-Off and Landing Aircraft

Online Deterministic 3D Trajectory Generation for Electric Vertical Take-Off and Landing Aircraft

Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

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

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