操控性橢圓理論於兩足機器人步態規劃之應用研究

Abstract

本論文以具有十個自由度之空間並聯式機構模擬KHR-1兩足機器人之下半身，並以操控性橢圓理論為核心，設計並模擬兩足機器人由蹲姿轉換至直立站姿及由站立姿態開始完成以兩左右跨步為一基礎步伐組之關節運動軌跡做為範例，進行電腦輔助軌跡規劃法的研發。在以程式完成軌跡設計後，透過控制器的數據傳輸介面將關節運動軌跡數據轉入KHR-1兩足機器人控制系統中，並藉由機器人執行動作範例以驗證理論推導之關節運動軌跡之實用性與穩定性。本研究所建立的兩足機器人步態規劃之流程，可簡化傳統程序的繁瑣耗時，同時提供一較為穩定可靠之動作模式。本研究所提出的方法為先推導出終端效應器特定點在卡氏座標中之線速度單位圓與關節角速度橢圓之對應轉換模型，經由計算找出終端效應器在往某特定方向移動時所對應各關節驅動器之最小角速度組合，以此最小角速度組合做為機械手作動規劃時之依據。本研究所採用的原理，在靜力學之觀點來看，每一單位時間間隔之角加速度變化較小。這使得兩足機器人運作時能獲得較高之穩定性。在機器人的姿態平衡的維持方面，關節角位移的計算規劃時輔以零矩點理論(Zero-Moment Point)建立機器人平衡機制。應用零矩點理論在兩足機器人的運動平衡控制方面，為維持機器人姿態對地面形成之合作用力向量通過零矩點且作用力接觸座標落在單腳腳底或雙腳間區域內便能使機器人獲得穩定的運動與姿態。本論文提出以操控性橢圓理論及零矩點理論作為核心概念建立輔助規劃與模擬系統規劃出兩足機器人之動作並進行穩定性與效率之分析。此外，本研究也實際組裝KHR-1多關節人形兩足機器人，經傳入所規劃的控制軌跡數據，進行作動測試。經實作測試，可確信本研究成果不僅可將多自由度的兩足機器人的控制軌跡規劃過程系統化與簡化，同時也可經由理論與模擬方法進行最佳化的規劃與應用。

Based on the manipulability ellipsoid algorithm, the research develops a gait planning system to generate the gait for the spatial parallel/serial type manipulator with ten or more degree of freedom. The research develops systematic methods for joint trajectory planning and simulation of the biped robot motion. The proposed methodology can be successfully applied to generate but not limited to the gaits of squat to stand and two walking strides. The desired joint trajectory of biped robot produced by developed program with the kernel of the manipulability ellipsoid algorithm. An appropriate procedure has been set up to transform the generated joint trajectory data to the control unit of the KHR-1 biped robot, after the simulation to test and verification of the robot on the motion stability. This proposed method can save the cycle-time on trajectory generation of the biped robot. The velocity ellipsoid method is currently adopted for finding the minimum combination of angular velocity of the joints of the robot. Based on the static kinematics, the manipulability ellipsoid method can provide the choice of the minimum variation of the joint velocity for the biped robot to reach the more stable motion status. Furthermore, Zero-Moment point algorithm is applied as the constraint of the restriction area of the projection point of the mass center of the robot in the state of trajectory planning, thus the high stability of the robot can be afforded. A biped robot KHR-1 with ten more degree of freedom has also been assembled and installed for proving the advantage and usefulness of the proposed method. The illustrated examples have demonstrated the benefit and the advantage on the gait planning of biped robot.