After an introductiou of the Plucker coordinate geometry, a discussion is made of the expression of screws in Plucker coordiuates and the addition of screws’ As a result, the geometry or geuerating gears is re-studie...After an introductiou of the Plucker coordinate geometry, a discussion is made of the expression of screws in Plucker coordiuates and the addition of screws’ As a result, the geometry or geuerating gears is re-studied and a formula is derived for calculating the axode leugth or hypoid gears’展开更多
In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondo...In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.展开更多
According to the theory that rotation transformation from the basecoordinate to an arbitrary one can be described by a single equivalent rotation about agiven rotational axis,it is proposed that the orientation of rob...According to the theory that rotation transformation from the basecoordinate to an arbitrary one can be described by a single equivalent rotation about agiven rotational axis,it is proposed that the orientation of robot can be described by usingthe vector of equivalent angular displacement.And the concept of pose motor and itsPlücker linear coordinate are established and used to describe the position and orientationof robot.Based on the fact that there is a one-to-one correspondence between the ori-ented straight lines in three-dimensional dual space,the interpolation plannings corre-sponding to the pose motors are developed in dual space.A new algorithm of robot CPmotion trajectory planning is presented.The correctness of the theory and derivation isconformed by an example.展开更多
文摘After an introductiou of the Plucker coordinate geometry, a discussion is made of the expression of screws in Plucker coordiuates and the addition of screws’ As a result, the geometry or geuerating gears is re-studied and a formula is derived for calculating the axode leugth or hypoid gears’
基金supported in part by the National Natural Science Foundation of China(51775385)the Natural Science Foundation of Shanghai(23ZR1466000)+3 种基金the Shanghai Industrial Collaborative Science and Technology Innovation Project(2021-cyxt2-kj10)the Innovation Program of Shanghai Municipal Education Commission(202101070007E00098)the Innovation Project of Engineering Research Center of Integration and Application of Digital Learning Technology of MOE(1221046)the Program to Cultivate Middle-Aged and Young Cadre Teacher of Jiangsu Province。
文摘In solving many-objective optimization problems(MaO Ps),existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure.Most candidate solutions become nondominated during the evolutionary process,thus leading to the failure of producing offspring toward Pareto-optimal front with diversity.Can we find a more effective way to select nondominated solutions and resolve this issue?To answer this critical question,this work proposes to evolve solutions through line complex rather than solution points in Euclidean space.First,Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones.Besides position vectors of the solution points,momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure.Then,a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distancebased estimator.Based on them,a novel many-objective evolutionary algorithm(MaOEA)is proposed by integrating a line complex-based environmental selection strategy into the NSGAⅢframework.The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives.Experimental results demonstrate its superior competitiveness in solving MaOPs.
文摘According to the theory that rotation transformation from the basecoordinate to an arbitrary one can be described by a single equivalent rotation about agiven rotational axis,it is proposed that the orientation of robot can be described by usingthe vector of equivalent angular displacement.And the concept of pose motor and itsPlücker linear coordinate are established and used to describe the position and orientationof robot.Based on the fact that there is a one-to-one correspondence between the ori-ented straight lines in three-dimensional dual space,the interpolation plannings corre-sponding to the pose motors are developed in dual space.A new algorithm of robot CPmotion trajectory planning is presented.The correctness of the theory and derivation isconformed by an example.
