別紙41 (課程博士(英文))Date of submission (month day, yeal')
Depar[ment ofStudenuD N1Ⅱ力ber

Mechanical Engineering

Prof. Naoki uchiyama

D1751BSupelvisors

Prof. Kentaro Takagi

Min set paing

へPP11Cant'5 namc

Abstract
Title ofThesis

07 05,2022(Doctor)

Spline・Based Approaches to Tilne・optimal, Smooth、 and High・ACCUI・acy
TI'aject01、y Generation for lndustrial Machines

Approx.80o words

CO】npuler numerical control machines and indus{rial manipulators are extensively used inmodern manufacturing industries to P引form various tasks 、vith compleX 御'ofiles that requh・ehigh・speed, high・accul'acy, and l'epeatability. Tasks are l'e御'esented as a σeonletric pl・0行le inthe canesian 、vorkspace, Genel'aⅡy, compleX 御'ofiles are separated into a series of lineal・
Seg1ηents by ule colnputer・aided lnanufacturing system. To avoid discontinuous motions at

the sharp con]el's of two Hnear segments, the nlachine has to colnpletely s{op the motion foreach seglnent,、¥hich consumes en引'gy and machining lime.1f lhe continuous feed rale isConsidered to transvel'se between segment trajectories, discontinU北ies of resulting traject01・ies
induce lnechanical 、vear and large tracking el'r01's by the contr011ers.

To enhance 桝'oductivity, the main objective is to complete the tasks h1 小e minimum motion

time. consequently, reseal'ch has explored to simultaneously improve the contradictm・yObjectives of motion tilne, such as slnoothness, consulned en伽'σ
energy, and acCⅢ・ac
accuracy of the、Ⅳ引、kpiece. Th引'efore, the Pω'eto optimal solution, which contributes a trade、off between

Contradict01'y objectives is getting attention by tl〕e decision makers nowadays. Due to theaccess limit of the 01'iginal contl'011ers and the complexity of the contl・ol stl・uctul・e, theadvanced contr011el's m'e sti11 difficult to i111Plemel]t for impl'oving the desired objectives ofindustl'ial madlines. Thel'ef01'e, the 01)tima11'eference trajectm'y genel・ation becomes a ke

dl'ivel' for its simplicity. Most imp01'tantly, the refel'ence motion trajectories must accurately
represent the geolnetl'ic path, be 飢 least continu011S in acce1引'ation, and satisfy the 1くinematicand dyna111ic linlits ofthe madlines f01' aⅡ horizons.

In lit固'ature, U〕e optilnal conu'0I PI'oblemS ω'e solYed by direct transcription lnethods, wh田・e
the machine limits are considel'ed as discl'ete constl'aints on σrid points for calculation alono
the traject引'y. As a dra、Nback, constraint violations may ocCⅢ'in、between the determined 01・idPoints. F01' complex pathS 圦ノith fl'cquendy changed derlvatives、 a larσe n山nb引・ of gridS ω・etypica11y requil'ed for constl'aint satisfaction; thus, the pl'obleln beconles computationaHy
expensive, and the optin〕ization solV引' may fail to find a feasible solution. Thel・efω・e, thisProcess is not su'aigl〕tfor、vard fm' usel'S. This thesis presents sevel'al approaches for sinole andmulti・objective slnootl] optimal traject01'y generations for industrial machines by contr01P雛'al〕)etel'ization of splines, gUω'anteeing kil]ematic constraints for the entire horizon

reg印'dless ofthe grid points.1Wo main approacheS ω'e anab乞ed in this study: decoupled. in、vhich tl〕e optimal conu'01 御'obleln is solved 、vitl] two steps of σeometl・ic path planning andtl'ajectⅨ'y optinlization, and coupled, in which the probleln is solved in a single step ofOptin〕ization. Literature review and preliminaries for u】is thesis a↑e discussed in chapter land 2、Chapter 3 and 4 PI'ovide the decoupled tl'aject01'y σenel'ations, assuming the oeometric paths

are predefined by a parametric curve or a set of via・points. The control P砥'alneterization isimplemented in terlns of B・splines to provide acceleration and jerk continuities. chapter 3
Presents the bi、objective optilnization problen〕 between the total motion and the jerk squareinteoral of motion trajectories in the time domain. Guaranteed kinematjc constl'ajnts areProposed based on the spline convex hUⅡS and the maxilnuln 3e0111etric derivatives along thePath. The pareto front comprising the signi丘Cant trade・off solutions is explored by theCombinations of nm'n〕alized normal constraint and divide and conquer algorithms. The

Simulations and experimental results validate that the proposed method provides anappl'oximately 3% faster and 21.57% 1esser average axial tl'acking el'rors than theConventiona11inear reparameterization method. chapter 4 discusses the time optimal contr01
Problem in the paramete↑ domain using the nonlinear transf01'mation of optin〕ization
Variables. The time dependency is excluded, and the optimal motion tilTle for each seg1れent

trajectory is independently achieved. The guaranteed kinematic constraints are determinedbased on the spline convex hU11S that Ⅱlnit the maximuln geometric derives between the10caⅡy affected intervals; therefm'e,1t iS 1110re relevant to apply on complex geometric patl〕S'Comparison with the jerk・1imited time・optimaltrajectory gena'ation shows that the proposed
method is more robust with the problen〕 grid size and gives a smoother time・optimaltrajectory, which reduces the aV剖'age axialtracking errors by approximately 12ツ0.
Chapter 5 Presents coupled optimaltrajectory generations by paramet引'ization of B・splines.
Time、optimal contour reshaping ofu〕e colnplex workpieces colnprising su'aight・Hne, circle,
and spHne contour se即nents is discussed in the first pal't. The velocity and acceleration
Continuity between segment trajectories, fitting accuracy ofthe geometric path, and kinematic
Constraints using spline convex hU11S are considered as constl'aints in the problem
forlnulation. The optimization results prove that the proposed method can represent various
G、code segments by considering the trade・off between the tilne・optilnality and fitting
accuracy of the workpiece' 1he second P釘't discusses the smooth trajectory generation for
reduced impact motion. Motion optimization is considered for the smooth catching of a aying
Object lvith a simHar velocity by lninimizing dle residualilnpact force between the object andthe industrial machine. The optimization results conarm that the l'esulting trajectories arebounded by kinelnatic and wm'kspace limits and satisfy the required velocity for the slnooth
Catching opa'ation. Fina11y, the conclusions for proposed spHne・based decoupled and coupled
Optimal trajectory gen剖'ationS ω'e drawn, and the expected fut山'e works m'e discussed inChapter 6.

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