Smooth path planning using biclothoid fillets for high speed CNC machines

Shahzadeh, Abbas; Khosravi, Abbas; Robinette, Troy; Nahavandi, Saeid

doi:10.1016/j.ijmachtools.2018.04.003

Cited by 43 publications

(13 citation statements)

References 30 publications

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“…Because of their monotone curvature variation, clothoid segments are of interest in diverse applications, including the design of highways and railways; path planning for mobile robots; specification of bipedal locomotion; control of unmanned aerial vehicles and autonomous ground vehicles; and smoothing of CNC machining toolpaths [4,21,24,28,30,31,37,38,39,41,42,44]. We are interested here in approximating canonical-form clothoid segments using Pythagorean-hodograph (PH) curves [13].…”

Section: Introductionmentioning

confidence: 99%

Approximation of monotone clothoid segments by degree 7 Pythagorean–hodograph curves

Farouki

Pelosi

Sampoli

2021

Journal of Computational and Applied Mathematics

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The clothoid is a planar curve with the intuitive geometrical property of a linear variation of the curvature with arc length, a feature that is important in many geometric design applications. However, the exact parameterization of the clothoid is defined in terms of the irreducible Fresnel integrals, which are computationally expensive to evaluate and incompatible with the polynomial/rational representations employed in computer aided geometric design. Consequently, applications that seek to exploit the simple curvature variation of the clothoid must rely on approximations that satisfy a prescribed tolerance. In the present study, we investigate the use of planar Pythagorean-hodograph (PH) curves as polynomial approximants to monotone clothoid segments, based on geometric Hermite interpolation of end points, tangents, and curvatures, and precise matching of the clothoid segment arc length. The construction, employing PH curves of degree 7, involves iterative solution of a system of five algebraic equations in five real unknowns. This is achieved by exploiting a closed-form solution to the problem of interpolating the specified data (except the curvatures) using quintic PH curves, to determine starting values that ensure rapid and accurate convergence to the desired solution.

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Section: Introductionmentioning

confidence: 99%

Approximation of monotone clothoid segments by degree 7 Pythagorean–hodograph curves

Farouki

Pelosi

Sampoli

2021

Journal of Computational and Applied Mathematics

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“…Recently, clothoid draws more attentions for local corner smoothing [30], [31], since it is the arclength-parameterized spline. It provides an analytical expression of the arclength.…”

Section: Introductionmentioning

confidence: 99%

“…It is more friendly for the on-line smoothing since more computing resources can be released to handle other tasks [6], [32]. However, the C 2 continuity leads to the discontinues jerk at the junction of the linear and curvilinear sub-paths and the junction of biclothoid [31]. The jerk jump at the junction of the biclothoid can be confined by calculating the critical velocity in the lookahead stage, whereas the jerk jump at the junction of linear and curvilinear splines is hard to control.…”

Section: Introductionmentioning

confidence: 99%

A Novel Local Smoothing Method for Five-Axis Machining With Time-Synchronization Feedrate Scheduling

et al. 2020

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This paper presents an analytical continuous smoothing method for the five-axis toolpath by simultaneously scheduling the tool position and tool orientation trajectories. In order to ensure the high-order continuous, the peak-controlled jerk and arclength-parameterized property, a novel curve ''airthoid'' is proposed for the first time. The biairthoid is involved to smooth the corners of the tool position in the workpiece coordinate system (WCS) and the corners of the tool orientation in the machine coordinate system (MCS), the geometries of which are analytically determined by the user-defined deviation errors. A time synchronization strategy is proposed to extend the duration of the predetermined cubic acceleration profile to a specified time. With the kinematic constraints of the tool position and the tool orientation, the transitional and rotational trajectories are analytically synchronized by sharing the same motion time. To comply with the constraints of the linear feed drives, an optimization strategy is conducted by adjusting the kinematics of the tool position. By doing so, the approximation errors of the tool position and tool orientation in the WCS are strictly satisfied. The analytical arclength expression of the smoothing curves is more suitable for the on-line interpolation. Due to the arclength-parametrized transition curve, the feedrate fluctuation is eliminated. With the proposed time synchronization strategy, the physical limits of the feed drives are all respected. Moreover, the high-order continuous airthoid makes the motion more smoothing-going. Simulations and experiments verify the effectiveness of the proposed algorithm.

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“…2 This addresses the shortcomings of CNC machine tools and serial robots, such as the inability to process special-shaped curved surfaces, the unadjustable rigidity of the support system, and the low processing efficiency and precision. 3–5 It is suitable for large-scale, aspherical, and precise optical mirror processing. Because optical mirror processing is a type of special precision machining, its accuracy is easily affected by human behavior, the inherent characteristics of the mechanism, and changes in environmental parameters.…”

Section: Introductionmentioning

confidence: 99%

Human-machine-environment information fusion and control compensation strategy for large optical mirror processing system

Jin

Chen

Guo

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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Large optical mirrors require an ultra-precise machining equipment, and a high level of surface-forming precision must be achieved. However, optical mirror processing systems (OMPSs) are susceptible to human behaviors, mechanical structural errors, and processing environments. The factors that affect quality include artificially formulated processes, slurry choice, joint friction, force-induced deformation, ambient temperature, and vibration interference. These factors can lead to a decrease in the accuracy of an OMPS. To study the influence of disturbances in the human-machine-environment (HME) on the OMPS, it is necessary to conduct a fusion analysis of the related factors. A parameter analysis is first conducted on the HME factors that influence the accuracy of OMPS. Then, the factors that influence the accuracy most significantly are determined. Subsequently, with the influencing factors as input parameters, and the output forces of the computer-controlled optical surface (CCOS) grinding system as the output parameters, the HME influencing factors are fused through a BP neural network optimized using a genetic algorithm, and the result is compared with that resulting from the original BP neural network fusion. Finally, according to the results of the fusion, environmental control of the processing system is performed, and the feedforward PD control compensation measures are established for the joint friction. An experimental analysis is also conducted to verify the effect of the information fusion and error compensation on the accuracy of the OMPS.

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Smooth path planning using biclothoid fillets for high speed CNC machines

Cited by 43 publications

References 30 publications

Approximation of monotone clothoid segments by degree 7 Pythagorean–hodograph curves

Approximation of monotone clothoid segments by degree 7 Pythagorean–hodograph curves

A Novel Local Smoothing Method for Five-Axis Machining With Time-Synchronization Feedrate Scheduling

Human-machine-environment information fusion and control compensation strategy for large optical mirror processing system

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