单足机器人周期跳跃控制的虚拟约束方法

 研究单足机器人周期跳跃控制问题．弹簧支撑倒立摆模型可以比较准确地描述动物的跳跃行为，但无控制的自然跳跃抗干扰能力较差，一般采用轨迹跟踪控制方法实现单足机器人周期跳跃．当系统存在比较大的误差时，传统的时间轨迹跟踪控制方法存在明显的不足．引入虚拟约束技术，采用基于空间路径跟踪的控制方法可以克服时间轨迹跟踪的不足．采用点足机器人模型，并通过控制腿伸缩的方式为系统提供动力，将跳跃过程分为地面摆动和腾空飞行两个阶段，并通过起飞和着陆两个事件完成两个阶段之间的转换，整个系统模型属于欠驱动非光滑动力学系统．根据简化的动力学方程获得系统的虚拟约束解析表达式，并采用部分反馈线性化方法结合PD 控制设计系统的控制律．分析了系统的混合零动力学方程，并证明了闭环系统的临界稳定性．仿真结果表明，提出的控制方法可以实现单足机器人的周期跳跃控制，并且对外部干扰具有较强的鲁棒性．

Virtual Constraints Approach for Periodic Hopping Control of a Monopod Robot

 The periodic jump control of a monopod robot is studied. Spring supported inverted pendulum model can accurately describe the jumping behaviour of animals, but the natural jumping without control has poor anti disturbance capability. Generally, trajectory tracking control method is used to realize the periodic hopping of a monopod robot. When the system has large error, the traditional time trajectory tracking control method has obvious shortcomings. The virtual constraint technology is introduced, and the space path tracking control method is used to overcome the shortcomings of time trajectory tracking control. The jumping process is divided into two stages, i.e., ground swing and flying, and the two events of take-off and landing are used to realize the transformations of the two stages. The system model belongs to underactuated non smooth dynamic system. According to the simplified dynamic equation, the analytical expression of virtual constraint is obtained, and the control law of the system is designed by partial feedback linearization and PD control. The hybrid zero dynamics of the system is analyzed, and the critical stability of the closed-loop system is proved. The simulation results show that the proposed control method can realize the periodic hopping control of the monopod robot and is robust to external disturbances.