Investigation of cutting mechanics in single point diamond turning of silicon

As a kind of brittle material, silicon will undergo brittle fracture at atmospheric pressure in conventional scale machining. Studies in the last two decades on hard and brittle materials including silicon, germanium, silicon nitride and silicon carbide have demonstrated ductile regime machining using single point diamond turning (SPDT) process. The mirror-like surface finish can be achieved in SPDT provided appropriate tool geometry and cutting parameters including feed rate, depth of cut and cutting speed are adopted.The research work in this thesis is based on combined experimental and numerical smoothed particle hydrodynamics (SPH) studies to provide an inclusive understanding of SPDT of silicon. A global perspective of tool and workpiece condition using experimental studies along with localized chip formation and stress distribution analysis using distinctive SPH approach offer a comprehensive insight of cutting mechanics of silicon and diamond tool wear. In SPH modelling of SPDT of silicon, the distribution of von Mises and hydrostatic stress at incipient and steady-state was found to provide the conditions pertinent to material failure, phase transformation, and ductile mode machining. The pressure-sensitive Drucker Prager (DP) material constitutive model was adopted to predict the machining response behaviour of silicon during SPDT. Inverse parametric analysis based on indentation test was carried out to determine the unknown DP parameters of silicon by analysing the loading-unloading curve for different DP parameters. A very first experimental study was conducted to determine Johnson-Cook (J-C) model constants for silicon. High strain rate compression tests using split Hopkinson pressure bar (SHPB) test as well as quasi-static tests using Instron fatigue testing machine were conducted to determine J-C model constants.The capability of diamond tools to maintain expedient conditions for high-pressure phase transformation (HPPT) as a function of rake angle and tool wear were investigated experimentally as well as using SPH approach. The proportional relationship of cutting forces magnitude and tool wear was found to differ owing to wear contour with different rake angles that influence the distribution of stresses and uniform hydrostatic pressure under the tool cutting edge. A new quantitative evaluation parameter for the tool wear resistance performance based on the cutting distance was also proposed. It was also found that the machinability of silicon could be improved by adopting novel surface defect machining (SDM) method.The ductile to brittle transition (DBT) with the progressive tool wear was found to initiate with the formation of lateral cracks at low tool wear volume which transform into brittle pitting damage at higher tool edge degradation. A significant variation in resistance to shear deformation as well as position shift of the maximum stress values was observed with the progressive tool wear. The magnitude and distribution of hydrostatic stress were also found to change significantly along the cutting edge of the new and worn diamond tools.As a kind of brittle material, silicon will undergo brittle fracture at atmospheric pressure in conventional scale machining. Studies in the last two decades on hard and brittle materials including silicon, germanium, silicon nitride and silicon carbide have demonstrated ductile regime machining using single point diamond turning (SPDT) process. The mirror-like surface finish can be achieved in SPDT provided appropriate tool geometry and cutting parameters including feed rate, depth of cut and cutting speed are adopted.The research work in this thesis is based on combined experimental and numerical smoothed particle hydrodynamics (SPH) studies to provide an inclusive understanding of SPDT of silicon. A global perspective of tool and workpiece condition using experimental studies along with localized chip formation and stress distribution analysis using distinctive SPH approach offer a comprehensive insight of cutting mechanics of silicon and diamond tool wear. In SPH modelling of SPDT of silicon, the distribution of von Mises and hydrostatic stress at incipient and steady-state was found to provide the conditions pertinent to material failure, phase transformation, and ductile mode machining. The pressure-sensitive Drucker Prager (DP) material constitutive model was adopted to predict the machining response behaviour of silicon during SPDT. Inverse parametric analysis based on indentation test was carried out to determine the unknown DP parameters of silicon by analysing the loading-unloading curve for different DP parameters. A very first experimental study was conducted to determine Johnson-Cook (J-C) model constants for silicon. High strain rate compression tests using split Hopkinson pressure bar (SHPB) test as well as quasi-static tests using Instron fatigue testing machine were conducted to determine J-C model constants.The capability of diamond tools to maintain expedient conditions for high-pressure phase transformation (HPPT) as a function of rake angle and tool wear were investigated experimentally as well as using SPH approach. The proportional relationship of cutting forces magnitude and tool wear was found to differ owing to wear contour with different rake angles that influence the distribution of stresses and uniform hydrostatic pressure under the tool cutting edge. A new quantitative evaluation parameter for the tool wear resistance performance based on the cutting distance was also proposed. It was also found that the machinability of silicon could be improved by adopting novel surface defect machining (SDM) method.The ductile to brittle transition (DBT) with the progressive tool wear was found to initiate with the formation of lateral cracks at low tool wear volume which transform into brittle pitting damage at higher tool edge degradation. A significant variation in resistance to shear deformation as well as position shift of the maximum stress values was observed with the progressive tool wear. The magnitude and distribution of hydrostatic stress were also found to change significantly along the cutting edge of the new and worn diamond tools

Sensor-Based Monitoring and Inspection of Surface Morphology in Ultraprecision Manufacturing Processes

This research proposes approaches for monitoring and inspection of surface morphology with respect to two ultraprecision/nanomanufacturing processes, namely, ultraprecision machining (UPM) and chemical mechanical planarization (CMP). The methods illustrated in this dissertation are motivated from the compelling need for in situ process monitoring in nanomanufacturing and invoke concepts from diverse scientific backgrounds, such as artificial neural networks, Bayesian learning, and algebraic graph theory. From an engineering perspective, this work has the following contributions:1. A combined neural network and Bayesian learning approach for early detection of UPM process anomalies by integrating data from multiple heterogeneous in situ sensors (force, vibration, and acoustic emission) is developed. The approach captures process drifts in UPM of aluminum 6061 discs within 15 milliseconds of their inception and is therefore valuable for minimizing yield losses.2. CMP process dynamics are mathematically represented using a deterministic multi-scale hierarchical nonlinear differential equation model. This process-machine inter-action (PMI) model is evocative of the various physio-mechanical aspects in CMP and closely emulates experimentally acquired vibration signal patterns, including complex nonlinear dynamics manifest in the process. By combining the PMI model predictions with features gathered from wirelessly acquired CMP vibration signal patterns, CMP process anomalies, such as pad wear, and drifts in polishing were identified in their nascent stage with high fidelity (R2 ~ 75%).3. An algebraic graph theoretic approach for quantifying nano-surface morphology from optical micrograph images is developed. The approach enables a parsimonious representation of the topological relationships between heterogeneous nano-surface fea-tures, which are enshrined in graph theoretic entities, namely, the similarity, degree, and Laplacian matrices. Topological invariant measures (e.g., Fiedler number, Kirchoff index) extracted from these matrices are shown to be sensitive to evolving nano-surface morphology. For instance, we observed that prominent nanoscale morphological changes on CMP processed Cu wafers, although discernible visually, could not be tractably quantified using statistical metrology parameters, such as arithmetic average roughness (Sa), root mean square roughness (Sq), etc. In contrast, CMP induced nanoscale surface variations were captured on invoking graph theoretic topological invariants. Consequently, the graph theoretic approach can enable timely, non-contact, and in situ metrology of semiconductor wafers by obviating the need for reticent profile mapping techniques (e.g., AFM, SEM, etc.), and thereby prevent the propagation of yield losses over long production runs.Industrial Engineering & Managemen

Mehatronički pristup pozicioniranju ultravisokih preciznosti i točnosti

Ultra-high precision mechatronics positioning systems are critical devices in current precision engineering and micro- and nano-systems’ technologies, as they allow repeatability and accuracy in the nanometric domain to be achieved. The doctoral thesis deals thoroughly with nonlinear stochastic frictional effects that limit the performances of ultra-high precision devices based on sliding and rolling elements. The state-of-the-art related to the frictional behavior in the pre-sliding and sliding motion regimes is considered and different friction models are validated. Due to its comprehensiveness and simplicity, the generalized Maxwell-slip (GMS) friction model is adopted to characterize frictional disturbances of a translational axis of an actual multi-degrees-of-freedom point-to-point mechatronics positioning system aimed at handling and positioning of microparts. The parameters of the GMS model are identified via innovative experimental set-ups, separately for the actuator-gearhead assembly and for the linear guideways, and included in the overall MATLAB/SIMULINK model of the used device. With the aim of compensating frictional effects, the modeled responses of the system are compared to experimental results when the system is controlled by means of a conventional proportional-integral-derivative (PID) controller, when the PID controller is complemented with an additional feed-forward model-based friction compensator and, finally, when the system is controlled via a self-tuning adaptive regulator. The adaptive regulator, implemented within the real-time field programmable gate array based control system, is proven to be the most efficient and is hence used in the final repetitive point-to-point positioning tests. Nanometric-range precision and accuracy (better than 250 nm), both in the case of short-range (micrometric) and long-range (millimeter) travels, are achieved. Different sensors, actuators and other design components, along with other control typologies, are experimentally validated in ultra-high precision positioning applications as well.Mehatronički sustavi ultra-visokih (nanometarskih) preciznosti i točnosti pozicioniranja su u današnje vrijeme vrlo važni u preciznom inženjerstvu i tehnologiji mikro- i nano-sustava. U disertaciji se temeljito analiziraju nelinearni stohastički učinci trenja koji vrlo često ograničavaju radna svojstva sustava za precizno pozicioniranje temeljenih na kliznim i valjnim elementima. Analizira se stanje tehnike za pomake pri silama manjim od sile statičkog trenja, kao i u režimu klizanja, te se vrednuju postojeći matematički modeli trenja. U razmatranom slučaju mehatroničkog sustava ultra-visokih preciznosti i točnosti pozicioniranja, namijenjenog montaži i manipulaciji mikrostruktura, trenje koje se javlja kod linearnih jednoosnih pomaka se, zbog jednostavnosti i sveobuhvatnosti toga pristupa, modelira generaliziranim Maxwell-slip (GMS) modelom trenja. Parametri GMS modela se identificiraju na inovativnim eksperimentalnim postavima, i to posebno za pokretački dio analiziranog sustava, koji se sastoji od istosmjernog motora s reduktorom, te posebno za linearni translator. Rezultirajući modeli trenja se zatim integriraju u cjeloviti model sustava implementiran u MATLAB/SIMULINK okruženju. S ciljem minimizacije utjecaja trenja, modelirani odziv sustava uspoređuje se potom s eksperimentalnim rezultatima dobivenim na sustavu reguliranom pomoću često korištenog proporcionalno-integralno-diferencijalnog (PID) regulatora, kada se sustav regulira po načelu unaprijedne veze, te kada se regulira prilagodljivim upravljačkim algoritmom. Regulator s prilagodljivim vođenjem, implementiran unutar stvarno-vremenskog sustava temeljenog na programibilnim logičkim vratima, pokazao se kao najbolje rješenje te se stoga koristi u uzastopnim eksperimentima pozicioniranja iz točke u točku, koji predstavljaju željenu funkcionalnost razmatranog sustava. Postignute su tako nanometarska preciznost i točnost (bolje od 250 nm) i to kako kod kraćih (mikrometarskih), tako i duljih (milimetarskih) pomaka. U završnom se dijelu disertacije eksperimentalno analizira i mogućnost korištenja drugih pokretača, osjetnika i strojnih elemenata kao i različitih upravljačkih pristupa pogodnih za ostvarivanje ultra-visokih preciznosti i točnosti pozicioniranja

Mehatronički pristup pozicioniranju ultravisokih preciznosti i točnosti

Ultra-high precision mechatronics positioning systems are critical devices in current precision engineering and micro- and nano-systems’ technologies, as they allow repeatability and accuracy in the nanometric domain to be achieved. The doctoral thesis deals thoroughly with nonlinear stochastic frictional effects that limit the performances of ultra-high precision devices based on sliding and rolling elements. The state-of-the-art related to the frictional behavior in the pre-sliding and sliding motion regimes is considered and different friction models are validated. Due to its comprehensiveness and simplicity, the generalized Maxwell-slip (GMS) friction model is adopted to characterize frictional disturbances of a translational axis of an actual multi-degrees-of-freedom point-to-point mechatronics positioning system aimed at handling and positioning of microparts. The parameters of the GMS model are identified via innovative experimental set-ups, separately for the actuator-gearhead assembly and for the linear guideways, and included in the overall MATLAB/SIMULINK model of the used device. With the aim of compensating frictional effects, the modeled responses of the system are compared to experimental results when the system is controlled by means of a conventional proportional-integral-derivative (PID) controller, when the PID controller is complemented with an additional feed-forward model-based friction compensator and, finally, when the system is controlled via a self-tuning adaptive regulator. The adaptive regulator, implemented within the real-time field programmable gate array based control system, is proven to be the most efficient and is hence used in the final repetitive point-to-point positioning tests. Nanometric-range precision and accuracy (better than 250 nm), both in the case of short-range (micrometric) and long-range (millimeter) travels, are achieved. Different sensors, actuators and other design components, along with other control typologies, are experimentally validated in ultra-high precision positioning applications as well.Mehatronički sustavi ultra-visokih (nanometarskih) preciznosti i točnosti pozicioniranja su u današnje vrijeme vrlo važni u preciznom inženjerstvu i tehnologiji mikro- i nano-sustava. U disertaciji se temeljito analiziraju nelinearni stohastički učinci trenja koji vrlo često ograničavaju radna svojstva sustava za precizno pozicioniranje temeljenih na kliznim i valjnim elementima. Analizira se stanje tehnike za pomake pri silama manjim od sile statičkog trenja, kao i u režimu klizanja, te se vrednuju postojeći matematički modeli trenja. U razmatranom slučaju mehatroničkog sustava ultra-visokih preciznosti i točnosti pozicioniranja, namijenjenog montaži i manipulaciji mikrostruktura, trenje koje se javlja kod linearnih jednoosnih pomaka se, zbog jednostavnosti i sveobuhvatnosti toga pristupa, modelira generaliziranim Maxwell-slip (GMS) modelom trenja. Parametri GMS modela se identificiraju na inovativnim eksperimentalnim postavima, i to posebno za pokretački dio analiziranog sustava, koji se sastoji od istosmjernog motora s reduktorom, te posebno za linearni translator. Rezultirajući modeli trenja se zatim integriraju u cjeloviti model sustava implementiran u MATLAB/SIMULINK okruženju. S ciljem minimizacije utjecaja trenja, modelirani odziv sustava uspoređuje se potom s eksperimentalnim rezultatima dobivenim na sustavu reguliranom pomoću često korištenog proporcionalno-integralno-diferencijalnog (PID) regulatora, kada se sustav regulira po načelu unaprijedne veze, te kada se regulira prilagodljivim upravljačkim algoritmom. Regulator s prilagodljivim vođenjem, implementiran unutar stvarno-vremenskog sustava temeljenog na programibilnim logičkim vratima, pokazao se kao najbolje rješenje te se stoga koristi u uzastopnim eksperimentima pozicioniranja iz točke u točku, koji predstavljaju željenu funkcionalnost razmatranog sustava. Postignute su tako nanometarska preciznost i točnost (bolje od 250 nm) i to kako kod kraćih (mikrometarskih), tako i duljih (milimetarskih) pomaka. U završnom se dijelu disertacije eksperimentalno analizira i mogućnost korištenja drugih pokretača, osjetnika i strojnih elemenata kao i različitih upravljačkih pristupa pogodnih za ostvarivanje ultra-visokih preciznosti i točnosti pozicioniranja

Design and Analysis of Long-Stroke Planar Switched Reluctance Motor for Positioning Applications

This paper presents the design, control, and experimental performance evaluation of a long-stroke planar switched reluctance motor (PSRM) for positioning applications. Based on comprehensive consideration of the electromagnetic and mechanical characteristics of the PSRM, a motor design is first developed to reduce the force ripple and deformation. A control scheme with LuGre friction compensation is then proposed to improve the positioning accuracy of the PSRM. Furthermore, this control scheme is proven to ensure the stable motion of the PSRM system. Additionally, the response speed and steady-state error of the PSRM system with this control scheme are theoretically analyzed. Finally, the experimental results are presented and analyzed. The effectiveness of the precision long-stroke motion of the PSRM and its promise for use in precision positioning applications are verified experimentally

An atomistic investigation on the nanometric cutting mechanism of hard, brittle materials

The demand for ultra precision machined devices and components is growing at a rapid pace in various areas such as the aerospace, energy, optical, electronics and bio-medical industries. Because of their outstanding engineering properties such as high refractive index, wide energy bandgap and low mass density, there is a continuing requirement for developments in manufacturing methods for hard, brittle materials. Accordingly, an assessment of the nanometric cutting of the optical materials silicon and silicon carbide (SiC), which are ostensibly hard and brittle, has been undertaken. Using an approach of parallel molecular dynamics simulations with a three-body potential energy function combined with experimental characterization, this thesis provides a quantitative understanding of the ductile-regime machining of silicon and SiC (polytypes: 3C, 4H and 6H SiC), and the mechanism by which a diamond tool wears during the process. The distinctive MD algorithm developed in this work provides a comprehensive analysis of thermal effects, high pressure phase transformation, tool wear (both chemical and abrasive), influence of crystal anisotropy, cutting forces and machining stresses (hydrostatic and von Mises), hitherto not done so far. The calculated stress state in the cutting zone during nanometric cutting of single crystal silicon indicated Herzfeld–Mott transition (metallization) due to high pressure phase transformation (HPPT) of silicon under the influence of deviatoric stress conditions. Consequently, the transformation of pristine silicon to β-silicon (Si-II) was found to be the likely reason for the observed ductility of bulk silicon during its nanoscale cutting. Tribochemical formation of silicon carbide through a solid state single phase reaction between the diamond tool and silicon workpiece in tandem with sp3-sp2 disorder of carbon atoms from the diamond tool up to a cutting temperature of 959 K has been suggested as the most likely mechanism through which a diamond cutting tool wears while cutting silicon. The recently developed dislocation extraction algorithm (DXA) was employed to detect the nucleation of dislocations in the MD simulations of varying cutting orientation and cutting direction. Interestingly, despite of being a compound of silicon and carbon, silicon carbide (SiC) exhibited characteristics more like diamond, e.g. both SiC iii workpiece and diamond cutting tool were found to undergo sp3-sp2 transition during the nanometric cutting of single crystal SiC. Also, cleavage was found to be the dominant mechanism of material removal on the (111) crystal orientation. Based on the overall analysis, it was found that 3C-SiC offers ease of deformation on either (111) , (110) or (100) setups. The simulated orthogonal components of thrust force in 3C-SiC showed a variation of up to 45% while the resultant cutting forces showed a variation of 37% suggesting that 3C-SiC is anisotropic in its ease of deformation. The simulation results for three major polytypes of SiC and for silicon indicated that 4H-SiC would produce the best sub-surface integrity followed by 3C-SiC, silicon and 6H-SiC. While, silicon and SiC were found to undergo HPPT which governs the ductility in these hard, brittle materials, corresponding evidence of HPPT during the SPDT of polycrystalline reaction bonded SiC (RB-SiC) was not observed. It was found that, since the grain orientation changes from one crystal to another in polycrystalline SiC, the cutting tool experiences work material with different crystallographic orientations and directions of cutting. Thus, some of the grain boundaries cause the individual grains to slide along the easy cleavage direction. Consequently, the cutting chips in RB-SiC are not deformed by plastic mechanisms alone, but rather a combination of phase transformation at the grain boundaries and cleavage of the grains both proceed in tandem. Also, the specific-cutting energy required to machine polycrystalline SiC was found to be lower than that required to machine single crystal SiC. Correspondingly, a relatively inferior machined surface finish is expected with a polycrystalline SiC. Based on the simulation model developed, a novel method has been proposed for the quantitative assessment of tool wear from the MD simulations. This model can be utilized for the comparison of tool wear for various simulation studies concerning graphitization of diamond tools. Finally, based on the theoretical simulation results, a novel method of machining is proposed to suppress tool wear and to obtain a better quality of the machined surface during machining of difficult-to-machine materials

Study and Performance Enhancement of Fast Tool Servo Diamond Turning of Micro-structured Surfaces

Ph.DDOCTOR OF PHILOSOPH

Mechatronic Design, Dynamics, Controls, and Metrology of a Long-Stroke Linear Nano-Positioner

Precision motion systems find a broad range of application in various fields such as micro/nano machining tools, lithography scanners, testing and metrology machines, micro-assembly, biotechnology, optics manufacturing, magnetic data-storage, and optical disk drives. In this thesis, an ultraprecision motion stage (nano-positioner) is designed and built based on the concept of a low-cost desktop precision micro machine tool. Linear positioning performance requirements of such a machine tool are used as design objectives. The nano-positioner’s mechatronic design is carried out in such a way to integrate different components towards high performance in terms of high dynamic range, high feedrate, servo accuracy, and geometric accuracy. A self-aligning air-bearing/bushing arrangement is employed for frictionless motion with infinite theoretical resolution, as well as reduced assembly costs and footprint. The air discharge from the air bearings/bushings are also utilized for assistance in the removal of heat dissipated from actuator coils. A voice coil actuator (VCA) is chosen for continuous, non-contact operation, and designed from scratch. A number of dimensional variables of the cylindrical VCA are set according to required forces, motion range, production/assembly tolerances, magnet availability, leakage flux, etc. The remainder of variables is determined according to two novel optimization objectives defined independent of the coil wire gauge, which separately aim for maximum stage acceleration capacity and minimum heat generation per generated force. The actuators are operated in a complementary double configuration for control simplicity which allows for a straightforward and robust design for controller stability. Controller design is carried out at current control and position control levels. Current frequency response of the voice coil actuators is obtained, and they are observed to possess additional high frequency dynamics on top of the expected first order lumped resistance and inductance model. These are attributed to the eddy currents in the stator structure. A closed loop bandwidth of better than 907 [Hz] is achieved using the integrator plus lead current controller. The position controller is designed using the identified overall plant which includes the moving body, current dynamics and the force response. The lead-lag position controller is tuned at 450 [Hz] cross-over frequency and 40 [deg] phase margin. The control error during the tracking of a step trajectory filtered at 40 [Hz] is found to vary between ±5 [nm], indicating a 4 million dynamic range over the 20 [mm] stroke length. Dynamic Error Budgeting (DEB) method has been used to resolve the components of the error, and the largest contributor is found to be the sensor noise. The actual positioning error, which is an ideal signal excluding sensor noise is estimated using the same methodology and disturbance models, and it is found to be 0.680 [nm] root-mean-square (RMS). For the trajectory following case, experiments are carried out with and without a compensation scheme for encoder quadrature detection errors. The compensation is observed to reduce the ±45 [nm] control error to ±15 [nm]. For the assessment of stage performance and the verification of design choices, modal testing and laser interferometric metrology have been applied to the linear nano-positioner. For modal testing, two independent methods are used and their predictions are compared. In the first method, a graphical approach, namely the peak-picking method, is employed to identify modal parameters (natural frequency and damping ratio) and mode shapes. In the second method, a modal testing software package is used to identify the same using automated algorithms. The first mode, which is the most critical one for controller design, is identified at 65 [Hz] as a roll mode, followed by horizontal, vertical, and pitch modes at 450, 484, and 960 [Hz], respectively. The geometric errors of the system are identified using laser interferometric measurements, using various optical setups for linear and angular components. An error budget is formed using these results, together with the estimated thermal errors and servo errors. The accuracy of the stage is determined to be ±5.0 [μm], which had a ±1.1 [μm] non-repeatable component. In the future, the controller structure can be enhanced with an additional pole beyond the crossover frequency, in order to suppress unnecessary oscillations of the control effort signal around the set point due to the encoder noise transmitted to the controller input. Using an estimation of air bearing pitch stiffness from the catalogue values for normal stiffness, the roll mode was predicted at 672 [Hz]. The much lower natural frequency for that mode identified in modal testing (65 [Hz]) can be attributed to the shortcomings of the estimation method, primarily the neglect of the distortion of the supporting air cushion at the bearing interface due to out of plane rotations. In the future, experimental data can be obtained to characterize the air bearing pitch stiffness more accurately. It was observed that the preferred compensation scheme for the encoder quadrature detection errors is unable to match third and fourth harmonics of the encoder measurement error sufficiently. In the future, better compensation methods can be investigated for an improved match. During laser interferometric measurements, measurement uncertainty due to laser beam misalignment and air turbulence were inferred to be high. In the future, better ways to align the laser with the optics, as well as methods for improved assessment and compensation of environmental effects can be investigated

Time-Optimal Control for High-Order Chain-of-Integrators Systems with Full State Constraints and Arbitrary Terminal States

Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrary given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further comprehension of the problem, this paper establishes a novel notation system and theoretical framework, successfully providing the switching manifold for high-order problems in the form of switching law. Through deriving properties of switching laws on signs and dimension, this paper proposes a definite condition for time-optimal control. Guided by the developed theory, a trajectory planning method named the manifold-intercept method (MIM) is developed. The proposed MIM can plan time-optimal jerk-limited trajectories with full state constraints, and can also plan near-optimal higher-order trajectories with negligible extra motion time. Numerical results indicate that the proposed MIM outperforms all baselines in computational time, computational accuracy, and trajectory quality by a large gap