雙載具協同推移物體之數學模型與模擬

Modeling and simulation for the Coordination of Two Mobile Robots in Pushing an Object

李璟和(Ching-Ho Li)

指導教授 ： 王立昇

共同指導教授 ： 張帆人

國立臺灣大學/工學院/應用力學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.01852

摘要

本文之主題為建構兩台載具協同推移物體之模型，並以模擬檢驗其合理性。為了讓物體能夠依照設定的軌跡移動，我們首先提出一個協同策略，利用分段式的B-樣條曲線(B-spline curve)以及幾何約束，設計出兩台載具的輪速，達到軌跡追蹤以及速度控制的目的。當載具在推移物體時，碰到了地面摩擦力分佈的問題，一般文獻中都將摩擦力假設成是均勻分佈，但這種假設會忽略掉摩擦力矩所造成的影響，不符合真實的物理現象。為解決此問題，我們利用摩擦力基本原理，將體上每一個單位面積所受的摩擦力分開計算，推導出地面非均勻摩擦力對剛體運動影響的表示式，再利用Appell方程推導整體系統的運動方程式。經由模擬結果顯示，我們所推導的協同策略以及動力模型，為可行且合理的。

關鍵字

非均勻摩擦 ； 雙載具 ； 協同運動

並列摘要

The theme of this thesis is to construct the dynamic model of a system consisting of two mobile robots pushing an object together, which is followed by the simulation to examine the suitability of the model. In order to move the object along a specified path, a coordination strategy to compute the rotation speeds of the wheels on the robots is designed based on the theory of B-spline curves and geometric constraints. When the robots are pushing the object on the surface, the friction inevitably appears which was traditionally assumed by a uniform distribution. However, such assumption may ignore the effect of frictional torque in some circumstances. In order to solve this problem, we use the basic principle for frictional force, and derive the non-uniform frictional force formula by separating the slender body into small pieces. The friction formula is then included in the dynamical equation which were deduced by applying the reduced Appell’s equation. Simulation results show that the proposed coordination strategy and the dynamical model are feasible and reasonable.

並列關鍵字

two mobile robots ； non-uniform friction ； pushing an object ； coordination

參考文獻

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