CAJ | 학술논문

针对传统denalit-hartenber (D-H)参数法进行机器人运动学建模存在的复杂性、奇异性以及逆运动学求解困难等问题,该文基于旋量理论建立了多自由度串联机器人的矩阵指数积(product-of-exponentials, POE)运动学模型,而同时旋量理论机器人逆运动学求解问题归结为高维非线性方程组的求解,于是引入希尔维斯特(sylvester)结式法进行逆运动学方程组求解,并在数学符号化运算Maple软件实现了逆解算法过程,最后通过实例计算表明,该逆运动学模型及求解方法高效准确可靠,物理和数学意义明确,实用性强,能够推广到其他构型机器人的运动学建模以及逆运动学的求解,为机器人逆运动学的快速求解提供了参考.
침대전통denalit-hartenber (D-H)삼수법진행궤기인운동학건모존재적복잡성、기이성이급역운동학구해곤난등문제,해문기우선량이론건립료다자유도천련궤기인적구진지수적(product-of-exponentials, POE)운동학모형,이동시선량이론궤기인역운동학구해문제귀결위고유비선성방정조적구해,우시인입희이유사특(sylvester)결식법진행역운동학방정조구해,병재수학부호화운산Maple연건실현료역해산법과정,최후통과실례계산표명,해역운동학모형급구해방법고효준학가고,물리화수학의의명학,실용성강,능구추엄도기타구형궤기인적운동학건모이급역운동학적구해,위궤기인역운동학적쾌속구해제공료삼고.
The traditional denalit-hartenber (D-H) method is very popular to set up kinematic model for robot, but this method has lots of disadvantages, which include complexity, singularity and difficulties in inverse kinematic model solving. therefore the kinematic model of six degree freedom robot using traditional denalit-hartenber (D-H) method, can not get the high precision for inverse solution, and make the robot instantaneity for working. This article applied a product-of-exponential (POE) kinematic model based on screw theory for multi-degree of freedom series robots. Firstly, we used the screw theory to set up model for every joint of robot; then put matrix of every joint model multiply, which could get the POE of kinematic model for multi degree of freedom series robot. As we known from the above, the screw theory method was not limited by the form of joint, and could set up the kinematic model of robot very conveniently. This method was applicable to all types of multi degree of freedom series robot with versatility. Then the sylvester resultant method was used to solve these equations. The sylvester resultant method could solve high-dimensional nonlinear equations in advantage, and get the result of the nonlinear equations fast. The process of solving was used Maple software to calculate, due to the Maple software can use the symbol instead of the number to algorithm. Finally, in order to prove this method was correct and useful, we got special data, which was put into the forward kinematics formula to calculate the terminal attitude of robot, then we put this result of terminal attitude into the inverse kinematics formula, and got turning angle of each joint for the 6R robot, which was correct in the result from the calculation. In order to prove this method is correct further, we calculated from the perspective of geometry, which was through the geometric relationship of the robot to calculate each joint turning angle, and this result was as the same. At last, this inverse kinematic model and solving method was proved as an efficient and accurate method by calculating an example. In general, this method has efficient, accurate, reliable, and clear significance at physical and mathematician, also can apply to other robots with differences in configuration in kinematic modeling and inverse kinematic solution, providing a reference to quickly solution in inverse kinematic of robots. Meanwhile, this method can improve the algorithm efficiency 30% more than the general method of elimination.