• Journal of Mechanical Science and Technology
• /
• 제20권10호
• /
• pp.1557-1566
• /
• 2006

We present a procedure for the application of global orthogonal polynomial into an atmospheric re-entry maneuvering problem. This trajectory optimization is imbedded in a family of canonically parameterized optimal control problem. The optimal control problem is transcribed to nonlinear programming via global orthogonal polynomial and is solved a sparse nonlinear optimization algorithm. We analyze the optimal trajectories with respect to the performance of re-entry maneuver.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2004년도 ICCAS
• /
• pp.1587-1592
• /
• 2004

In the area of tracking control, it is important to design not only the controllers but also the trajectories to which a system has to follow. Position in the form of the $5^{th}$ order polynomial is often used with constraints of initial and final states. Smooth ending with possible minimum time is important for many systems to be away from vibrations or jerky motions. A simple polynomial-like trajectory generation method based on zero final state constraints is suggested and named ZSPOT. The effects of suggested method are shown through experiments in which a system follows an easy and computationally light reference trajectory.

• 전기학회논문지
• /
• 제58권9호
• /
• pp.1827-1833
• /
• 2009

This paper deals with the trajectory tracking control of wheeled mobile robots with input constraint. The proposed method converts the trajectory tracking problem to the system stability problem using the control inputs composed of feedforward and feedback terms, and then, by using Taylor series, nonlinear terms in origin system are transformed into polynomial equations. The composed system model can make it possible to obtain the control inputs using numerical tool named as SOSTOOL. From the simulation results, the mobile robot can track the reference trajectory well and can have faster convergence rate of the trajectory errors than the existing nonlinear control method. By using the proposed method, we can easily obtain the control input for nonlinear systems with input constraint.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2003년도 ICCAS
• /
• pp.101-106
• /
• 2003

In the area of tracking control, it is important to design not only the controllers but also the trajectories to which a system has to follow. $5^{th}$ order polynomial is often used with constraints of initial and final states. Smooth ending with possible minimum time is important for many systems because of vibration or jerky motions. Examples are increased with development of technology in smaller, more accurate systems. On the base of a polynomial like trajectory generation method from a paper in ACC2002 and RIC(Robust Internal-loop Compensator) control scheme of Robotics and Bio-mechanics lab. of POSTECH, generalized and expanded polynomial like trajectory generation method is showed.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 26-27 Oct. 1990
• /
• pp.135-139
• /
• 1990

In general, the control of robot arms falls into two board categories (position control and force control). The joint interpolated trajectory schemes generally interpolate the desired joint path by a class of polynomial functions and generate a sequence of time based control set points for the control of a manipulator from a initial location to its destination. A digital position controller was designed and adapted to the industrial balancing manipulator. And also, the joint interpolated trajectory using 3rd order polynomial was generated in this study. The IBM PC used as the main controller and the trajectory planner had enough run-time capabilities. The 8097BH microcontroller is an integral pan of the joint controller which directly controls an axis of motion. The PI servo control system to treat each joint of the robot arm as a independent joint servo mechanism had satisfying performance, and a sequence of time-based intermediate configurations of the manipulator hand showed good continuity and smoothness on position and velocity of the manipulator's joint coordinates along the trajectory.

• 동력기계공학회지
• /
• 제21권5호
• /
• pp.41-47
• /
• 2017

To implement Argentina tango dancer-like walking of the humanoid robot, a new trajectory generation scheme based on particle swarm optimization of the blending polynomial is presented. Firstly, the characteristics of Argentina tango walking are derived from observation of tango dance. Secondly, these are reflected in walking pose conditions and cost functions of particle swarm optimization to determine the coefficients of blending polynomial. For the stability of biped walking, zero moment point and reference trajectory of swing foot are also included in cost function. Thirdly, after tango walking cycle is divided into 3 stages with 2 postures, optimal trajectories of ankles, knees and hip of lower body, which include 6 sagittal and 4 coronal angles, are derived in consequence of optimization. Finally, the feasibility of the proposed scheme is validated by simulating biped walking of humanoid robot with derived trajectories under the 3D Simscape environment.

• 한국항공우주학회지
• /
• 제45권8호
• /
• pp.662-670
• /
• 2017

본 논문에서는 한국형 달 착륙 임무를 위한 아폴로 유도 법칙의 파라미터 선정을 위한 최적화 기반의 절차를 제안하였다. 달 착륙 문제를 연료 소모량을 최소화하기 위한 궤적 최적화 문제로 공식화하였으며 비행 이전 단계에서 본 문제를 풀어 착륙선의 기준 궤적을 획득할 수 있다. 아폴로 유도의 파라미터들은 유도 명령을 정의하기 위해 사용되는 다항식의 계수들이며, 비행 이전 단계에서 구해진 기준 궤적을 기반으로 선정된다. 제안된 절차의 효과를 입증하기 위해, 본 절차를 사용한 한국형 달 착륙 임무의 착륙 유도 사례연구를 수행하였다.

• Animal Bioscience
• /
• 제37권5호
• /
• pp.817-825
• /
• 2024

Objective: The aim of this study was to identify suitable polynomial regression for modeling the average growth trajectory and to estimate the relative development of the rib eye area, scrotal circumference, and morphometric measurements of Guzerat young bulls. Methods: A total of 45 recently weaned males, aged 325.8±28.0 days and weighing 219.9±38.05 kg, were evaluated. The animals were kept on Brachiaria brizantha pastures, received multiple supplementations, and were managed under uniform conditions for 294 days, with evaluations conducted every 56 days. The average growth trajectory was adjusted using ordinary polynomials, Legendre polynomials, and quadratic B-splines. The coefficient of determination, mean absolute deviation, mean square error, the value of the restricted likelihood function, Akaike information criteria, and consistent Akaike information criteria were applied to assess the quality of the fits. For the study of allometric growth, the power model was applied. Results: Ordinary polynomial and Legendre polynomial models of the fifth order provided the best fits. B-splines yielded the best fits in comparing models with the same number of parameters. Based on the restricted likelihood function, Akaike's information criterion, and consistent Akaike's information criterion, the B-splines model with six intervals described the growth trajectory of evaluated animals more smoothly and consistently. In the study of allometric growth, the evaluated traits exhibited negative heterogeneity (b<1) relative to the animals' weight (p<0.01), indicating the precocity of Guzerat cattle for weight gain on pasture. Conclusion: Complementary studies of growth trajectory and allometry can help identify when an animal's weight changes and thus assist in decision-making regarding management practices, nutritional requirements, and genetic selection strategies to optimize growth and animal performance.

• 한국음향학회지
• /
• 제19권3호
• /
• pp.35-44
• /
• 2000

본 논문에서는 음성 패턴을 효율적으로 모델링하고자 분절 특징(segmental feature)을 이 용하여 은닉 마코프 모델(hidden markov model)의 일반적인 형식에 기반한 새로운 모수적 궤적 모델 (parametric trajectory model)을 제안한다. 일반적으로 벡터의 열로써 표현되는 분절은 관측 열의 궤적(trajectory)으로 표현된다. 이 궤적은 연속적인 프레임들의 전이 정보(transitional information)를 표현하는 디자인 행렬을 이용하여 얻어지며, 다항식의 회귀 함수(polynomial regression function)로써 나타낼 수 있다. 이러한 궤적을 HMM에 적용하기 위해서 프레임 특징 대신 분절의 특성 을 표현하는 궤적으로 대치하고 우도(likelihood) 계산에 궤적들의 비교에 의한 확률 값을 반영시켜야 한다. 본 논문에서는 궤적간의 유사도를 측정하는 분절 우도(segment likelihood)와 모델을 구성하는 궤적변수의 추정 알고리즘을 제안한다. 임의의 분절에 대한 관측 확률은 제안된 분절 우도와 궤적의 추정 오차(estimation error of trajectories)의 곱으로써 표현된다. 궤적의 추정 오차는 상태에서 주어진 분절 우도의 가중치로 표현될 수 있으며, 이 가중치는 궤적과 대응되는 분절의 적합도를 표현하는 확률을 나타낸다. 본 논문에서 제 안된 모델은 일반적 인 HMM과 모수적 궤적 모델의 일반화(generalization) 또는 확장(extension) 모델로 생각될 수 있다. 본 모델의 성능을 평가하기 위하여 TIMIT 데이터에 기반한 실험을 한 결과, 분절 길이(segment length)와 회귀 차수(regression order)가 변할수록 일반적인 HMM에 비하여 뚜렷한 성능향상이 있음을 알 수 있었다.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1989년도 추계학술대회 논문집 학회본부
• /
• pp.462-466
• /
• 1989

This paper describes the methods of spline low-order polynomial trajectory planning using only a few limited look-ahead knots on the desired trajectory for the real-time computing. Specifically presented are the mixed joint trajectory planning methods which apply linear or LSPB method to initial and finial segments, overlapped cubic spline method to the other segments, where the displacements for initial and finial segments are chosen to be relatively smaller than the displacements for the other, equidistant segments. Experimental and simulation results of these methods show smooth motions and improved path tracking performances compared with any other interpolated joint trajectory planning methods.