This study investigates a planar differential game involving a singular attacker and defender,wherein the attacker endeavors to arrive at a specified target line while the defender seeks to intercept prior to this occ...This study investigates a planar differential game involving a singular attacker and defender,wherein the attacker endeavors to arrive at a specified target line while the defender seeks to intercept prior to this occurrence.The game is formulated with explicit boundary conditions,and the derivation of optimal strategies for both participants is conducted by examining the geometric characteristics of the reachable sets and terminal configurations.In contrast to traditional pursuit-evasion games,which utilize point or circular targets,the introduction of a target line presents unique geometric intricacies that complicate the determination of interception conditions.Analytical solutions for optimal controls are derived,accompanied by a lucid geometric interpretation of terminal states.The proposed formulation not only broadens the reach-avoid framework to encompass line-type targets but also offers theoretical guidance for practical defense scenarios involving extended boundaries.Ultimately,the analysis of this simplified single-attacker-single-defender scenario provides a foundational basis for future explorations into multi-agent defense systems.展开更多
基于单树随机树搜索算法(Single directional rapidly-exploring random tree,single-RRT)和双树随机树搜索算法(Bi-directional rapidly-exploring random tree,bi-RRT),对7R机械臂的避障达点运动规划展开系统研究。基于single-RRT算...基于单树随机树搜索算法(Single directional rapidly-exploring random tree,single-RRT)和双树随机树搜索算法(Bi-directional rapidly-exploring random tree,bi-RRT),对7R机械臂的避障达点运动规划展开系统研究。基于single-RRT算法进行避障达点运动的数值仿真和实物样机试验。提出一种新的bi-RRT算法,结合末端姿态调整和关节自运动来生成目标树。并利用7R机械臂的解析逆解,生成目标位形。传统的bi-RRT算法只给定了一个目标位形,而新算法中目标点树根是由一群目标位形组成。在给定的障碍物环境中,机器人自动选择某一合适的位形作为目标节点来引导搜索树最有效地生长。通过数值仿真,验证该方法的优越性。利用Matlab和C++的混合编程和OpenGL开发了7R机械臂避障达点运动规划仿真软件。利用该软件,对基于bi-RRT的7R机械臂避障达点运动规划进行虚拟样机的试验研究。展开更多
文摘This study investigates a planar differential game involving a singular attacker and defender,wherein the attacker endeavors to arrive at a specified target line while the defender seeks to intercept prior to this occurrence.The game is formulated with explicit boundary conditions,and the derivation of optimal strategies for both participants is conducted by examining the geometric characteristics of the reachable sets and terminal configurations.In contrast to traditional pursuit-evasion games,which utilize point or circular targets,the introduction of a target line presents unique geometric intricacies that complicate the determination of interception conditions.Analytical solutions for optimal controls are derived,accompanied by a lucid geometric interpretation of terminal states.The proposed formulation not only broadens the reach-avoid framework to encompass line-type targets but also offers theoretical guidance for practical defense scenarios involving extended boundaries.Ultimately,the analysis of this simplified single-attacker-single-defender scenario provides a foundational basis for future explorations into multi-agent defense systems.
文摘基于单树随机树搜索算法(Single directional rapidly-exploring random tree,single-RRT)和双树随机树搜索算法(Bi-directional rapidly-exploring random tree,bi-RRT),对7R机械臂的避障达点运动规划展开系统研究。基于single-RRT算法进行避障达点运动的数值仿真和实物样机试验。提出一种新的bi-RRT算法,结合末端姿态调整和关节自运动来生成目标树。并利用7R机械臂的解析逆解,生成目标位形。传统的bi-RRT算法只给定了一个目标位形,而新算法中目标点树根是由一群目标位形组成。在给定的障碍物环境中,机器人自动选择某一合适的位形作为目标节点来引导搜索树最有效地生长。通过数值仿真,验证该方法的优越性。利用Matlab和C++的混合编程和OpenGL开发了7R机械臂避障达点运动规划仿真软件。利用该软件,对基于bi-RRT的7R机械臂避障达点运动规划进行虚拟样机的试验研究。
