Search results for: motion synthesis

Authors: G. Çelik Gül, F. Kurtuluş

Abstract:

The first laboratory synthesis of hard materials such as diamond proceeded to attack of developing materials with high hardness to compete diamond. Boron rich solids are good candidates owing to their short interatomic bond lengths and strong covalent character. Boron containing hard material was synthesized by modifiedmicrowave method under nitrogen atmosphere by using a fuel (glycine or urea), amorphous boron and/or boric acid in appropriate molar ratio. Characterizations were done by x-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy/energy dispersive analyze (SEM/EDS), thermo gravimetric/differential thermal analysis (TG/DTA).

Keywords: Boron containing materials, hard materials, microwave synthesis, powder X-ray diffraction.

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Authors: Oleksandr Poliakov, Olena Chepenyuk, Yevgen Pashkov, Mykhaylo Kalinin, Vadym Kramar

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In one of the prosthesis designs for lower limb transfemoral amputations artificial knee joints with polycentric mechanisms are used. Such prostheses are characterized by high stability during the stance phase of the movement. The existing variety of polycentric mechanisms indicates the possibility of finding the optimal prosthesis design satisfying several quality criteria.In this paper we present a multicriteria method for the synthesis of the artifical polycentric knee mechanism based on the uniform systematic study of the design parameters space and on the analysis of Pareto optimal solutions.

Keywords: Optimalcriteria, polycentric knee, prosthesis, synthesis, transfemoral amputee.

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Authors: Jasmin Velagic, Nedim Osmic, Bakir Lacevic

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In this paper the neural network-based controller is designed for motion control of a mobile robot. This paper treats the problems of trajectory following and posture stabilization of the mobile robot with nonholonomic constraints. For this purpose the recurrent neural network with one hidden layer is used. It learns relationship between linear velocities and error positions of the mobile robot. This neural network is trained on-line using the backpropagation optimization algorithm with an adaptive learning rate. The optimization algorithm is performed at each sample time to compute the optimal control inputs. The performance of the proposed system is investigated using a kinematic model of the mobile robot.

Keywords: Mobile robot, kinematic model, neural network, motion control, adaptive learning rate.

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Authors: N. Tugrul, F. T. Senberber, A. S. Kipcak E. Moroydor Derun, S. Piskin

Abstract:

In this research, it is aimed not only microwave synthesis of magnesium borates but also evaluation of magnesium wastes. Synthesis process can be described with the reaction of Mg wastes and boric acid using microwave energy. X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR) were applied to synthesized minerals. According to XRD results, magnesium borate hydrate mixtures were obtained as mcallisterite (pdf# = 01-070-1902, Mg₂(B₆O₇(OH)₆)₂.9(H₂O)) at higher crystallinity properties was achieved at the mole ratio raw material 1:1. Also, other kinds of magnesium borate hydrates were obtained at lower crystallinity such as admontite (pdf # = 01-076-0540, MgO(B₂O₃)₃.7(H₂O)), inderite (pdf # = 01-072-2308, 2MgO.3B₂O₃.15(H₂O)) and magnesium borate hydrates (pdf # = 01-076-0539, MgO(B₂O₃)₃.6(H₂O)). FT-IR spectrums indicated that minor changes were seen at the band values of characteristic stretching in each experiment. At the end of experiments it is seen that using microwave energy may contribute positive effects to design of synthesis process such as reducing reaction time and products at higher crystallinity.

Keywords: Magnesium wastes, boric acid, magnesium borate, microwave energy.

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Authors: Dr.K.Sri Rama Krishna, J.Lakshmi Narayana, Dr.L.Pratap Reddy

Abstract:

Microstrip lines, widely used for good reason, are broadband in frequency and provide circuits that are compact and light in weight. They are generally economical to produce since they are readily adaptable to hybrid and monolithic integrated circuit (IC) fabrication technologies at RF and microwave frequencies. Although, the existing EM simulation models used for the synthesis and analysis of microstrip lines are reasonably accurate, they are computationally intensive and time consuming. Neural networks recently gained attention as fast and flexible vehicles to microwave modeling, simulation and optimization. After learning and abstracting from microwave data, through a process called training, neural network models are used during microwave design to provide instant answers to the task learned.This paper presents simple and accurate ANN models for the synthesis and analysis of Microstrip lines to more accurately compute the characteristic parameters and the physical dimensions respectively for the required design specifications.

Keywords: Neural Models, Algorithms, Microstrip Lines, Analysis, Synthesis

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Authors: P. Sanzo

Abstract:

Increased physical fitness participation has been paralleled by increasedoveruse injuries such as insertional Achilles tendinosis (AT). Treatment has provided inconsistentresults. The use of extracorporeal shockwave therapy (ECSWT) offers a new treatment consideration.The purpose of this study was to assess the effects of ECSWTon pain, function, range of motion (ROM), joint mobility and strength in patients with AT. Thirty subjects were treated with ECSWT and measures were takenbefore and three months after treatment. There was significant differences in visual analog scale (VAS) scores for pain at rest (p=0.002); after activity (p= 0.0001); overall improvement(p=0.0001); Lower Extremity Functional Scale (LEFS) scores (p=0.002); dorsiflexion range of motion (ROM) (p=0.0001); plantarflexion strength (p=0.025); talocrural joint anterior glide (p=0.046); and subtalar joint medial and lateral glide (p=0.025).ECSWT offers a new intervention that may limit the progression of the disorder and the long term healthcare costs associated with AT.

Keywords: Extracorporeal shockwave therapy, shockwave therapy, Achilles tendinosis, range of motion, strength, joint mobility

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Authors: Dhiraj Dolai, Rupayan Bhattacharya

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In this study, a comparison of Range Of Motion (ROM) of middle and long-distance runners and swimmers has been made. The mobility of the various joints is essential for the quick movement of any sportsman. Knowledge of a ROM helps in preventing injuries, in repeating the movement, and in generating speed and power. ROM varies among individuals, and it is influenced by factors such as gender, age, and whether the motion is performed actively or passively. ROM for running and swimming, both performed with due consideration on speed, plays an important role. The time of generation of speed and mobility of the particular joints are very important for both kinds of athletes. The difficulties that happen during running and swimming in the direction of motion is changed. In this study, data were collected for a total of 102 subjects divided into three groups: control group (22), middle and long-distance runners (40), and swimmers (40), and their ages are between 12 to 18 years. The swimmers have higher ROM in shoulder joint flexion, extension, abduction, and adduction movement. Middle and long-distance runners have significantly greater ROM from Control Group in the left shoulder joint flexion with a 5.82 mean difference. Swimmers have significantly higher ROM from the Control Group in the left shoulder joint flexion with 24.84 mean difference and swimmers have significantly higher ROM from the Middle and Long distance runners in left shoulder flexion with 19.02 mean difference. The picture will be clear after a more detailed investigation.

Keywords: Range of motion, runners, swimmers, significance.

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Authors: Hamid Yasinian

Abstract:

Random epistemologies and hash tables have garnered minimal interest from both security experts and experts in the last several years. In fact, few information theorists would disagree with the evaluation of expert systems. In our research, we discover how flip-flop gates can be applied to the study of superpages. Though such a hypothesis at first glance seems perverse, it is derived from known results.

Keywords: Synthesis, Multi-Processors, Interactive Model, Moor’s Law.

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Authors: H. Loukil, A. Ben Atitallah, F. Ghozzi, M. A. Ben Ayed, N. Masmoudi

Abstract:

In MPEG and H.26x standards, to eliminate the temporal redundancy we use motion estimation. Given that the motion estimation stage is very complex in terms of computational effort, a hardware implementation on a re-configurable circuit is crucial for the requirements of different real time multimedia applications. In this paper, we present hardware architecture for motion estimation based on "Full Search Block Matching" (FSBM) algorithm. This architecture presents minimum latency, maximum throughput, full utilization of hardware resources such as embedded memory blocks, and combining both pipelining and parallel processing techniques. Our design is described in VHDL language, verified by simulation and implemented in a Stratix II EP2S130F1020C4 FPGA circuit. The experiment result show that the optimum operating clock frequency of the proposed design is 89MHz which achieves 160M pixels/sec.

Keywords: SAD, FSBM, Hardware Implementation, FPGA.

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Authors: S. Aouabdi, M. Taibi

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This paper presents powerful techniques for the development of a new monitoring method based on multi-scale entropy (MSE) in order to characterize the behaviour of the concentrations of different gases present in the synthesis of Ammonia and soft-sensor based on Principal Component Analysis (PCA).

Keywords: Ammonia synthesis, concentrations of different gases, soft sensor, multi-scale entropy, multivariate statistics.

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Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

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This paper focuses on the critical components of the situational awareness (SA), the controls of position and orientation of an autonomous surface vessel (ASV). Moving of vessel into desired area in particular sea is a challenging but important task for ASVs to achieve high level of autonomy under adverse conditions. With the SA strategy, the approach motion by neural control of an initial stage of an ASV trajectory using neural network predictive controller and the circular motion by control of yaw moment in the final stage of trajectory were proposed. This control system has been demonstrated and evaluated by simulation of maritime maneuvers using software package Simulink. From the simulation results it can be seen that the fast SA of similar ASVs with economy in energy can be asserted during the maritime missions in search-and-rescue operations.

Keywords: Autonomous surface vessels, neurocontrollers, situational awareness.

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Authors: K. Raghuwaiya, S. Singh, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon, in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios.

Keywords: Artificial potential fields, 3-trailer systems, motion planning, posture, parking and collision-free trajectories.

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Authors: Kei Fujii, Jun Okawa, Kaori Suigetsu

Abstract:

Concatenative speech synthesis is a method that can make speech sound which has naturalness and high-individuality of a speaker by introducing a large speech corpus. Based on this method, in this paper, we propose a voice conversion method whose conversion speech has high-individuality and naturalness. The authors also have two subjective evaluation experiments for evaluating individuality and sound quality of conversion speech. From the results, following three facts have be confirmed: (a) the proposal method can convert the individuality of speakers well, (b) employing the framework of unit selection (especially join cost) of concatenative speech synthesis into conventional voice conversion improves the sound quality of conversion speech, and (c) the proposal method is robust against the difference of genders between a source speaker and a target speaker.

Keywords: concatenative speech synthesis, join cost, speaker individuality, unit selection, voice conversion

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Authors: Sun Li-ping, Zhu Jian-xun, Liu Sheng-nan

Abstract:

In order to study the performance of dynamic positioning system during S-lay operations, dynamic positioning system is simulated with the hull-stinger-pipe coupling effect. The roller of stinger is simulated by the generalized elastic contact theory. The stinger is composed of Morrison members. Force on pipe is calculated by lumped mass method. Time domain of fully coupled barge model is analyzed combining with PID controller, Kalman filter and allocation of thrust using Sequential Quadratic Programming method. It is also analyzed that the effect of hull wave frequency motion on pipe-stinger coupling force and dynamic positioning system. Besides, it is studied that how S-lay operations affect the dynamic positioning accuracy. The simulation results are proved to be available by checking pipe stress with API criterion. The effect of heave and yaw motion cannot be ignored on hull-stinger-pipe coupling force and dynamic positioning system. It is important to decrease the barge’s pitch motion and lay pipe in head sea in order to improve safety of the S-lay installation and dynamic positioning.

Keywords: S-lay operation, dynamic positioning, coupling motion; time domain, allocation of thrust.

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Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

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In this paper, we propose a solution to the motion control problem of a 2-link revolute manipulator arm. We require the end-effector of the arm to move safely to its designated target in a priori known workspace cluttered with fixed circular obstacles of arbitrary position and sizes. Firstly a unique velocity algorithm is used to move the end-effector to its target. Secondly, for obstacle avoidance a turning angle is designed, which when incorporated into the control laws ensures that the entire robot arm avoids any number of fixed obstacles along its path enroute the target. The control laws proposed in this paper also ensure that the equilibrium point of the system is asymptotically stable. Computer simulations of the proposed technique are presented.

Keywords: 2-link revolute manipulator, motion control, obstacle avoidance, asymptotic stability.

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Authors: Jian Huang, Weixin Qian, Hongfang Ma, Haitao Zhang, Weiyong Ying

Abstract:

Cobalt catalysts were supported on extruded silica carrier and different-type (SiO₂, γ-Al₂O₃) commercial supports with different shapes and sizes to produce heavy hydrocarbons for Fischer-Tropsch synthesis. The catalysts were characterized by N₂ physisorption and H₂-TPR. The catalytic performance of the catalysts was tested in a fixed bed reactor. The results of Fischer-Tropsch synthesis performance showed that the cobalt catalyst supported on spherical silica supports displayed a higher activity and a higher selectivity to C₅⁺ products, due to the fact that the active components were only distributed in the surface layer of spherical carrier, and the influence of gas diffusion restriction on catalytic performance was weakened. Therefore, it can be concluded that the eggshell cobalt catalyst was superior to precious metals modified catalysts in the synthesis of heavy hydrocarbons.

Keywords: Fischer-Tropsch synthesis, cobalt catalyst, support shape, heavy hydrocarbons.

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Authors: Riku Hayashida, Tomoaki Hashimoto

Abstract:

This paper provides a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. Underwater robots are expected to be used for various work assignments. The large variety of applications of underwater robots motivates researchers to develop control systems and technologies for underwater robots. Several control methods have been proposed so far for the stabilization of nominal system model of underwater robots with no parameter uncertainty. Parameter uncertainties are considered to be obstacles in implementation of the such nominal control methods for underwater robots. The objective of this study is to establish a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: Robust control, stabilization method, underwater robot, parameter uncertainty.

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Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva

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In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.

Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.

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Authors: Ming Cong, Yinghua Wu, Dong Liu, Haiying Wen, Junfa Yu

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In order to improve control performance and eliminate steady, a coupling compensation for 6-DOF parallel robot is presented. Taking dynamic load Tank Simulator as the research object, this paper analyzes the coupling of 6-DOC parallel robot considering the degree of freedom of the 6-DOF parallel manipulator. The coupling angle and coupling velocity are derived based on inverse kinematics model. It uses the mechanism-model combined method which takes practical moving track that considering the performance of motion controller and motor as its input to make the study. Experimental results show that the coupling compensation improves motion stability as well as accuracy. Besides, it decreases the dither amplitude of dynamic load Tank Simulator.

Keywords: coupling compensation, screw theory, parallel robot, mechanism-model combined motion

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Authors: T. C. Manjunath, C. Ardil

Abstract:

This paper presents an efficient method of obtaining a straight-line motion in the tool configuration space using an articulated robot between two specified points. The simulation results & the implementation results show the effectiveness of the method.

Keywords: Bounded deviation algorithm, Straight line motion, Tool configuration space, Joint space, TCV.

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Authors: Anton Stadler, Thorsten Ike

Abstract:

In this paper, we present a video based smoke detection algorithm based on TVL1 optical flow estimation. The main part of the algorithm is an accumulating system for motion angles and upward motion speed of the flow field. We optimized the usage of TVL1 flow estimation for the detection of smoke with very low smoke density. Therefore, we use adapted flow parameters and estimate the flow field on difference images. We show in theory and in evaluation that this improves the performance of smoke detection significantly. We evaluate the smoke algorithm using videos with different smoke densities and different backgrounds. We show that smoke detection is very reliable in varying scenarios. Further we verify that our algorithm is very robust towards crowded scenes disturbance videos.

Keywords: Low density, optical flow, upward smoke motion, video based smoke detection.

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Authors: E. Moroydor Derun, P. Gurses, M. Yildirim, A. S. Kipcak, T. Ibroska, S. Piskin

Abstract:

Due to their strong mechanical and thermal properties magnesium borates have a wide usage area such as ceramic industry, detergent production, friction reducing additive and grease production. In this study, microwave synthesis of magnesium borates from MgCl₂.6H₂O (Magnesium chloride hexahydrate), MgO (Magnesium oxide) and H₃BO₃ (Boric acid) for different reaction times is researched. X-ray Diffraction (XRD) and Fourier Transform Infrared (FT-IR) Spectroscopy are used to find out how the reaction time sways on the products. The superficial properties are investigated with Scanning Electron Microscopy (SEM). According to XRD analysis, the synthesized compounds are 00-041-1407 pdf coded Shabinite (Mg₅(BO₃)₄Cl₂(OH)₅.4(H₂O)) and 01-073-2158 pdf coded Karlite (Mg₇(BO₃)₃(OH,Cl)₅).

Keywords: Magnesium borate, microwave synthesis, XRD, SEM.

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Authors: Nikolaos Kroupis, Minas Dasygenis, Dimitrios Soudris, Antonios Thanailakis

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One of the most growing areas in the embedded community is multimedia devices. Multimedia devices incorporate a number of complicated functions for their operation, like motion estimation. A multitude of different implementations have been proposed to reduce motion estimation complexity, such as spiral search. We have studied the implementations of spiral search and identified areas of improvement. We propose a modified spiral search algorithm, with lower computational complexity compared to the original spiral search. We have implemented our algorithm on an embedded ARM based architecture, with custom memory hierarchy. The resulting system yields energy consumption reduction up to 64% and performance increase up to 77%, with a small penalty of 2.3 dB, in average, of video quality compared with the original spiral search algorithm.

Keywords: Spiral Search, Motion Estimation, Embedded Systems, Low Power

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Authors: S. Mat Radzi, W.A.F. Mustafa, S.S Othman, H.M. Noor

Abstract:

Nowadays, butyl acetate, a pineapple flavor has been applied widely in food, beverage, cosmetic and pharmaceutical industries. In this study, Butyl acetate, a flavor ester was successfully synthesized via green synthesis of enzymatic reaction route. Commercial immobilized lipase from Rhizomucor miehei (Lipozyme RMIM) was used as biocatalyst in the esterification reaction between acetic acid and butanol. Various reaction parameters such as reaction time (RT), temperature (T) and amount of enzyme (E) were chosen to optimize the reaction synthesis in solvent-free system. The optimum condition to produce butyl acetate was at reaction time (RT), 18 hours; temperature (T), 37°C and amount of enzyme, 25 % (w/w of total substrate). Analysis of yield showed that at optimum condition, >78 % of butyl acetate was produced. The product was confirmed as butyl acetate from FTIR analysis whereby the presence of an ester group was observed at wavenumber of 1742 cm-1.

Keywords: Butyl acetate, immobilized enyzme, esterification, flavor ester, green synthesis

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Authors: Peter Antwi Buah, Yingbin Zhang, Jianxian He, Chenlin Xiang, Delali Atsu Y. Bakah

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Near-fault ground motions with velocity pulses are considered to cause significant damage to structures or slopes compared to ordinary ground motions without velocity pulses. The double pulsed pulse-like ground motion is well known to be stronger than the single pulse. This research has numerically justified this perspective by studying the dynamic response of a homogeneous rock slope subjected to four pulse-like and two non-pulse-like ground motions using the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) software. Two of the pulse-like ground motions just have a single pulse. The results show that near-fault ground motions with velocity pulses can cause a higher dynamic response than regular ground motions. The amplification of the peak ground acceleration (PGA) in horizontal direction increases with the increase of the slope elevation. The seismic response of the slope under double pulse ground motion is stronger than that of the single pulse ground motion. The PGV amplification factor under the effect of the non-pulse-like records is also smaller than those under the pulse-like records. The velocity pulse strengthens the earthquake damage to the slope, which results in producing a stronger dynamic response.

Keywords: Velocity pulses, dynamic response, PGV magnification effect, elevation effect, double pulse.

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Authors: Francisco J. Lopez-Jaquez, Sandra E. Ramirez-Jara

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This paper presents an implementation and performance test of a distributed motion control system based on a master-slave configuration used to move a plasma-cutting torch over a predefined trajectory. The master is a general-purpose computer running on an open source operating system platform and software developer. Software running in the master computer generates commands on real time and we measure performance based on a selected set of differences between expected and observed distances. We are testing the null hypothesis that the outcome trajectory is identical to the input against the alternative hypothesis that there is a shift to the right or left of the input one. We used the Wilcoxon signed ranks test method for the hypothesis test.

Keywords: Distributed, motion, control, real-time, contouring.

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Authors: Mohamed Ali KAMMOUN, Ahmed Ben HAMIDA

Abstract:

In this paper, we present a novel statistical approach to corpus-based speech synthesis. Classically, phonetic information is defined and considered as acoustic reference to be respected. In this way, many studies were elaborated for acoustical unit classification. This type of classification allows separating units according to their symbolic characteristics. Indeed, target cost and concatenation cost were classically defined for unit selection. In Corpus-Based Speech Synthesis System, when using large text corpora, cost functions were limited to a juxtaposition of symbolic criteria and the acoustic information of units is not exploited in the definition of the target cost. In this manuscript, we token in our consideration the unit phonetic information corresponding to acoustic information. This would be realized by defining a probabilistic linguistic Bi-grams model basically used for unit selection. The selected units would be extracted from the English TIMIT corpora.

Keywords: Unit selection, Corpus-based Speech Synthesis, Bigram model

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Authors: N. Tugrul, A. S. Kipcak, E. MoroydorDerun, S. Piskin

Abstract:

Zinc borate is an important boron compound that can be used as multi-functional flame retardant additive due to its high dehydration temperature property. In this study, theraw materials of ZnSO₄.7H₂O, NaOH and H₃BO₃werecharacterized by X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR) and used in the synthesis of zinc borates.The synthesis parameters were set to 100°C reaction temperature and 120 minutes of reaction time, with different molar ratio of starting materials (ZnSO₄.7H₂O:NaOH:H₃BO₃). After the zinc borate synthesis, the identifications of the products were conducted by XRD and FT-IR. As a result,Zinc Oxide Borate Hydrate [Zn₃B₆O₁₂.3.5H₂O], were synthesized at the molar ratios of 1:1:3, 1:1:4, 1:2:5 and 1:2:6. Among these ratios 1:2:6 had the best results.

Keywords: Zinc borate, ZnSO4.7H2O, NaOH, H3BO3, XRD, FT-IR.

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Authors: Carolina Gouveia, José Vieira, Pedro Pinho

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The cardiopulmonary signal monitoring, without the usage of contact electrodes or any type of in-body sensors, has several applications such as sleeping monitoring and continuous monitoring of vital signals in bedridden patients. This system has also applications in the vehicular environment to monitor the driver, in order to avoid any possible accident in case of cardiac failure. Thus, the bio-radar system proposed in this paper, can measure vital signals accurately by using the Doppler effect principle that relates the received signal properties with the distance change between the radar antennas and the person’s chest-wall. Once the bio-radar aim is to monitor subjects in real-time and during long periods of time, it is impossible to guarantee the patient immobilization, hence their random motion will interfere in the acquired signals. In this paper, a mathematical model of the bio-radar is presented, as well as its simulation in MATLAB. The used algorithm for breath rate extraction is explained and a method for DC offsets removal based in a motion detection system is proposed. Furthermore, experimental tests were conducted with a view to prove that the unavoidable random motion can be used to estimate the DC offsets accurately and thus remove them successfully.

Keywords: Bio-signals, DC Component, Doppler Effect, ellipse fitting, radar, SDR.

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Authors: Nemat Abazari, Ilgin Sager

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In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, Rigid body motion, Lorentz metric.

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