Dynamic Modeling And Application Research On The Articulated Multibody System With Second-Order Nonholonomic Contraints

The common characteristic of rootless multibody system (without fixed base) and underactuated multibody system is that the quantity of control input is less than that of generalized coordinates. The constraint equations of configuration space can't satisfy the control request of system certain motions, but due to the dynamic coupling between joints, the dynamic constraints can be applied to the system control. These dynamic constraint equations are second-order differential equations and not integral in general, therefore these two multibody systems are essentially dynamic systems with second-order nonholonomic constraints. The paper investigates the dynamics modeling of this second-order nonholonomic systems, and analyses the coupled motion of redundant mobile robots, underactuated compliant mechanism and space manipulator system based on the nonholonomic constraint equations. The main research contents are as follows:(1)The kinematics of underactuated aritculated multi-body systems with elastic energy storage joints is analyzed, and a dynamic model of underactuated system is built based on D'Alembert-Lagrange principle. They provide the foundations for the analysis of dynamic characteristics and the motion control of the high redundancy underactuated robots with nonholonomic constraints.(2)Through adding the dynamic nominal mechanism between the rootless aritculated multi-body system and the ground reference frame, such nonholonomic multi-body system is converted into underactuated articulated multi-body system with fixed base; the second-order nonholonomic constraint equations of the system and the acceleration expressions of nominal and actual joints are derived based on the decoupling form of the dynamic model; based on the definition of joint angular acceleration output precision indices, the constraint characteristic of the nominal mechanism is analyzed and the influence of system parameters on the output is discussed.(3)Based on the dynamic nominal mechanism method, the dynamic model of the serpentine locomotion of elastic underactuated snake-like robot is built, and the nonholonomic constraint equations of passive joints are derived; based on the definition of the performance indices for describing the coupling motion of passive joint, the effect of kinematics, dynamics parameters and the stiffness and damping characteristics of elastic energy storage element and other factors on coupling characteristic of the elastic underactuated snake-like robot are discussed.(4)Taking the J-type bionic foot as an example, the pseudo-rigid-segments partition method is proposed based on the geometrical shape and stiffness distribution of compliant components, and the J-type foot pseudo-rigid-body modeling is built; therefore, the compliant mechanism is equivalent to a underactuated articulated multi-body system with elastic energy storage joints; based on force analysis and dynamics nominal mechanism method, the dynamic modeling of J-foot is established, and the nonholonomic constraint equations of the equivalent joint acceleration of pseudo-rigid body model is derived; on the basis of the definition of the performance indices of force/torque transmission and the coupling action, the effect of the structure parameters of the J-type foot and the end force on locomotion characteristic is discussed.(5)Based on the dynamic nominal mechanism method, the dynamic nominal mechanisms between the space manipulator system and orbit coordinate are added, and the first and second order effect coefficients of the system are given based on Lie group, Lie algebra, the dynamic model is built; the acceleration constraint equations of the carrier are derived, the coupling motion performance indices are defined, and the effect of the arm structural parameters on the carrier coupling motion performance is discussed(6)Based on the snake-like robot prototype, motion path planning control and experiments researches of a actual rootless multibody system are investigated; the coupling torque of servomotors of the prototype is analyzed based on the analysis of spatial linkage mechanism kinematics and serpentine crawling path planning; the experiments confirm that the robot is of ability to realize several motion modes, including lateral undulation, left and right turning motions, and uplifting head.