Path planning with Pythagorean-hodograph curves for unmanned or autonomous vehicles

Farouki, Rida T.; Giannelli, Carlotta; Mugnaini, Duccio; Sestini, Alessandra

doi:10.1177/0954410017690550

Cited by 13 publications

(9 citation statements)

References 31 publications

(93 reference statements)

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“…In order to obtain the PH curve with continuous curvature, the quantic PH curve was used as the path for each UAV in this paper. The theory and calculation method of the PH curve were not repeated here, relevant contents can be found in [29,30]. It should be noted that the kinematics constraint of a UAV is satisfied by bounding the curvature of the PH curve in a two-dimensional plane, so the maximum curvature on a flyable PH curve should satisfy:…”

Section: Pythagorean Hodograph Curvementioning

confidence: 99%

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A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition

et al. 2019

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A hierarchical mission planning method was proposed to solve a simultaneous attack mission planning problem for multi-unmanned aerial vehicles (UAVs). The method consisted of three phases aiming to decouple and solve the mission planning problem. In the first phase, the Pythagorean hodograph (PH) curve was used in the path estimation process for each UAV, which also served as the input for the task allocation process. In the second phase, a task allocation algorithm based on a negotiation mechanism was proposed to assign the targets. Considering the resource requirement, time-dependent value of targets and resource consumption of UAVs, the proposed task allocation algorithm can generate a feasible allocation strategy and get the maximum system utility. In the last phase, a path planning method was proposed to generate a simultaneous arrival PH path for each UAV considering UAV’s kinematic constraint and collision avoidance with obstacles. The comparison simulations showed that the path estimation process using the PH curve and the proposed task allocation algorithm improved the system utility, and the hierarchical mission planning method has potential in a real mission.

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Section: Pythagorean Hodograph Curvementioning

confidence: 99%

“…The length of the PH curve was used in this paper. J smooth denotes the cost function of the smoothness of the generated path, which can be expressed by the elastic energy of the generated PH curve [29].…”

Section: Path Estimationmentioning

confidence: 99%

A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition

et al. 2019

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“…In addition, the Pythagorean-Hodograph (PH) curve has other advantages, for example, the curve has finite extremum curvature [24,25]. Due to the special property of the PH curve, it is widely used in path planning [26,27], obstacle avoidance [28], continuum manipulators [29], highways and railways design [30,31], and many other fields [32]. Researchers proposed interpolation methods of a PH curve of degree nine, however, it puts more emphasis on geometric issues, and the calculation of real-time interpolators is rather complicated [33].…”

Section: Introductionmentioning

confidence: 99%

Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Liang

2019

Applied Sciences

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A new trajectory planning approach on the basis of the quintic Pythagorean–Hodograph (PH) curve is presented and applied to Delta robot for implementing pick-and-place operation (PPO). To satisfy a prescribed geometrical constraint, which indicates the distance between the transition segment curve and right angle of PPO trajectory is no greater than a prescribed value, the quintic PH curve is used to produce a connection segment path for collision avoidance. The relationship between the PH curve and constraint is analyzed, based on which PH curve is calculated simply. Afterwards, the trajectory is planned in different phases with different motion laws, i.e. polynomial motion laws and PH curve parameter-dependent motion laws, to obtain a smooth performance both in Cartesian and joint space. The relationship between the PH curve and constraint is also used to improve the efficiency of calculation, and the trajectory symmetry is used to reduce calculation time by direct symmetric transformation. Thus, real-time performance is improved. The results of simulations and experiments indicate that the approach in this paper can provide smooth motion and meet the real-time requirement under the prescribed geometrical constraint.

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“…It may be shown [10] that expressions (13) and (14) are both non-negative at the smaller root of (11). When u, v, w are determined from (10) and (12), the complex coefficients (9) are known, and are multiplied by |∆q| exp(i In general, the procedure provides two formal solutions (corresponding to the two feasible sign pairs α, β) to the problem of matching the specified data, of which one has an attractive shape, while the other exhibits an undesirable looping behavior -the latter can be discarded on the basis of a higher value for the elastic bending energy [8] or absolute rotation index [18].…”

Section: Planar Pythagorean-hodograph Curvesmentioning

confidence: 99%

“…This feature facilitates exact computations of various properties required to satisfy geometrical or physical path constraints -such as bounds on path curvature or climb angle, avoidance of obstacles, and maintenance of safe vehicle separations. An overview of the capabilities of PH curves within the context of UAV path planning may be found in [13].…”

Section: Introductionmentioning

confidence: 99%

Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles

Farouki

2017

Computer Aided Geometric Design

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A helical curve, or curve of constant slope, offers a natural flight path for an aerial vehicle with a limited climb rate to achieve an increase in altitude between prescribed initial and final states. Every polynomial helical curve is a spatial Pythagorean-hodograph (PH) curve, and the distinctive features of the PH curves have attracted growing interest in their use for Unmanned Aerial Vehicle (UAV) path planning. This study describes an exact algorithm for constructing helical PH paths, corresponding to a constant climb rate at a given speed, between initial and final positions and motion directions. The algorithm bypasses the more sophisticated algebraic representations of spatial PH curves, and instead employs a simple "lifting" scheme to generate helical PH paths from planar PH curves constructed using the complex representation. In this context, a novel scheme to construct planar quintic PH curves that interpolate given end points and tangents, with exactly prescribed arc lengths, plays a key role. It is also shown that these helical paths admit simple closed-form rotation-minimizing adapted frames. The algorithm is simple, efficient, and robust, and can accommodate helical axes of arbitrary orientation through simple rotation transformations. Its implementation is illustrated by several computed examples.

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Path planning with Pythagorean-hodograph curves for unmanned or autonomous vehicles

Cited by 13 publications

References 31 publications

A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition

A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition

Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles

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