• 제어로봇시스템학회논문지
• /
• 제19권6호
• /
• pp.540-546
• /
• 2013

This paper presents a trajectory planning algorithm for TMR (Two-wheeled Mobile Robots). The trajectory is developed in joint space and considers the physical limits of a TMR. First, we present a process for generating a smooth curve through a Bezier curve. The trajectory for the center of the TMR following the Bezier curve is developed through a convolution operator taking into consideration its physical limits. The trajectory along the Bezier curve is regenerated using time-dependent parameters which correspond to the distance driven by the velocity of the center of the TMR in a sampling time. The velocity commands in the Cartesian space are converted to actuator commands for two wheels. In case that the actuator commands exceed the maximum velocity, the trajectory is redeveloped with compensated center velocity. We also suggest a smooth trajectory planning algorithm in joint space for the two segmented paths. Finally, the effectiveness of the algorithm is shown through numerical examples and application to a simulator.

• 대한수학회지
• /
• 제55권6호
• /
• pp.1359-1380
• /
• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• 대한수학회보
• /
• 제35권4호
• /
• pp.757-767
• /
• 1998

For a Riemannian manifold $(M^n, g)$ we consider the space $V(M^n, g)$ of all smooth functions on $M^n$ whose Hessian is proportional to the metric tensor $g$. It is well-known that if $M^n$ is a space form then $V(M^n)$ is of dimension n+2. In this paper, conversely, we prove that if $V(M^n)$ is of dimension $\ge{n+1}$, then $M^n$ is a Riemannian space form.

• 대한수학회논문집
• /
• 제5권2호
• /
• pp.79-86
• /
• 1990

• 대한수학회논문집
• /
• 제8권4호
• /
• pp.699-707
• /
• 1993

• East Asian mathematical journal
• /
• 제25권1호
• /
• pp.27-37
• /
• 2009

In this paper, we introduce an iterative method for a pair of nonexpansive mappings. Strong convergence theorems are established in a real uniformly smooth Banach space.

• East Asian mathematical journal
• /
• 제24권1호
• /
• pp.57-65
• /
• 2008

The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제11권4호
• /
• pp.293-308
• /
• 2004

Let K be a nonempty convex subset of an arbitrary Banach space X and $T\;:\;K\;{\rightarrow}\;K$ be a uniformly continuous strictly hemi-contractive operator with bounded range. We prove that certain Ishikawa iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. We also establish similar convergence and almost stability results for strictly hemi-contractive operator $T\;:\;K\;{\rightarrow}\;K$, where K is a nonempty convex subset of arbitrary uniformly smooth Banach space X. The convergence results presented in this paper extend, improve and unify the corresponding results in Chang [1], Chang, Cho, Lee & Kang [2], Chidume [3, 4, 5, 6, 7, 8], Chidume & Osilike [9, 10, 11, 12], Liu [19], Schu [25], Tan & Xu [26], Xu [28], Zhou [29], Zhou & Jia [30] and others.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제23권4호
• /
• pp.301-327
• /
• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.

• 한국항공우주학회지
• /
• 제39권12호
• /
• pp.1124-1132
• /
• 2011

본 논문에서는 2차원 공간에서 기동하는 고정익 무인항공기의 장애물 회피를 위한 부드러운 경로궤적을 생성하는 문제를 다룬다. 2차원 장애물맵의 이산화 모델링을 위해 육각형 격자를 채택하였고, 이는 사각형 격자에 비해 연결성이 높아 부드러운 경로궤적 생성이 가능하도록 하였다. 특히 본 논문에서 제안된 경로템플릿 기법은 일정거리 단위로 조합 가능한 대표경로들(경로템플릿)을 사용하여 무인항공기의 기준경로를 생성하는 방법이고, 온라인 경로궤적 생성에서 계산량을 줄여 메모리 및 연산리소스가 제한되는 소형 오토파일럿에서도 적용이 가능하다는 장점이 있다.