INVESTIGATION ON KANE DYNAMIC EQUATIONSBASED ON SCREW THEORY FOR OPEN-CHAIN MANIPULATORS

First,screw theory,product of exponential formulas and Jacobian matrix are introduced.Then definitions are given about active force wrench,inertial force wrench,partial velocity twist,generalized active force,and generalized inertial force according to screw theory.After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived. Later on how to compute the partial velocity twist by geometrical method is illustrated. Finally the correctness of conclusions is verified by example.

KANE’S EQUATIONS FOR PERCUSSION MOTION OF VARIABLE MASS NONHOLONOMIC MECHANICAL SYSTEMS

In this paper,the Kane’s equations for the Routh’s form of variable massnonholonomic systems are established.and the Kane’s equations for percussion motionof variable mass holonomic and nonholonomic systems are deduced from them. Secondly,the equivalence to Lagrange’s equations for percussion motion and Kane’sequations is obtained,and the application of the new equation is illustrated by anexample.

Dynamics and adaptive control of a dual-arm space robot with closed-loop constraints and uncertain inertial parameters

A dynamics-based adaptive control approach is proposed for a planar dual-arm space robot in the presence of closed-loop constraints and uncertain inertial parameters of the payload. The controller is capable of controlling the po- sition and attitude of both the satellite base and the payload grasped by the manipulator end effectors. The equations of motion in reduced-order form for the constrained system are derived by incorporating the constraint equations in terms of accelerations into Kane＇s equations of the unconstrained system. Model analysis shows that the resulting equations perfectly meet the requirement of adaptive controller design. Consequently, by using an indirect approach, an adaptive control scheme is proposed to accomplish position/attitude trajectory tracking control with the uncertain parameters be- ing estimated on-line. The actuator redundancy due to the closed-loop constraints is utilized to minimize a weighted norm of the joint torques. Global asymptotic stability is proven by using Lyapunov＇s method, and simulation results are also presented to demonstrate the effectiveness of the proposed approach.

Attitude Coordination of Multi-HUG Formation Based on Multibody System Theory

Application of multiple hybrid underwater gliders （HUGs） is a promising method for large scale, long-term ocean survey. Attitude coordination has become a requisite for task execution of multi-HUG formation. In this paper, a multibody model is presented for attitude coordination among agents in the HUG formation. The HUG formation is regarded as a multi-rigid body system. The interaction between agents in the formation is described by artificial potential field （APF） approach. Attitude control torque is composed of a conservative torque generated by orientation potential field and a dissipative term related with angular velocity. Dynamic modeling of the multibody system is presented to analyze the dynamic process of the HUG formation. Numerical calculation is carried out to simulate attitude synchronization with two kinds of formation topologies. Results show that attitude synchronization can be fulfilled based on the multibody method described in this paper. It is also indicated that different topologies affect attitude control quality with respect to energy consumption and adjusting time. Low level topology should be adopted during formation control scheme design to achieve a better control effect.

Dynamic Model of Underwater Snake-Like Robot Using Kane's Method

In this paper, a dynamic model for an underwater snake-like robot is developed based on Kane's dynamic equations. This methodology allows construction of the dynamic model simply and incrementally. The partial velocity is deduced. The forces which contribute to dynamics are determined by Kane's approach. The generalized active forces and the generalized inertia forces are deduced. The model developed in this paper includes inertia force, inertia moment, gravity, control torques, and three major hydrodynamic forces: added mass, profile drag and buoyancy. The equations of hydrodynamic forces are deduced. Kane's method provides a direct approach for incorporating external environmental forces into the model. The dynamic model developed in this paper is obtained in a closed form which is well suited for control purposes. It is also computationally efficient and has physical insight into what forces really influence the system dynamics. The simulation result shows that the proposed method is feasible.

A Dynamic Model of an Underwater Quadruped Walking Robot Using Kane's Method

In this paper, the kinematics and dynamics of an underwater quadruped walking robot were derived based on Kane dynamic equations. This methodology allows construction of the dynamic model simply and incrementally. The velocity and angular velocity components of an underwater quadruped walking robot were served as the generalized velocities. The forces which contribute to dynamics of an underwater quadruped walking robot were determined by Kane's approach. The equations of hydrodynamic forces of an underwater quadruped walking robot were deduced. Hydrodynamic coefficients were determined by experiments. The dynamic model was established by obtaining the generalized active forces and the generalized inertia forces. Numerical simulations of the walking behavior on underwater flat ground were implemented to verify the dynamic model of an underwater quadruped walking robot. Simulation results show that the dynamic model is correct.

Dynamic modeling of a 6-degree-of-freedom Stewart platform driven by a permanent magnet synchronous motor

For an electrical six-degree-of-freedom Stewart platform,it is difficult to compute the equivalent inertia of each motor in real time,as the inertia is time-varying.In this study,an analysis using Kane's equation is undertaken of the driven torque of the movements of motor systems(including motor friction,movements of motor systems along with the actuators,rotation around axis of rotors and snails),as well as driven torque of the platform and actuators.The electromagnetic torque was calculated according to vector-controlled permanent magnet synchronous motor(PMSM) dynamics.By equalizing the driven torque and electromagnetic torque,a model was established.This method,taking into consideration the influence of counter electromotive force(EMF) and motor friction,could be applied to the real-time dynamic control of the platform,through which the calculation of the time-varying equivalent inertia is avoided.Finally,simulations with typically desired trajectory inputs are presented and the performance of the Stewart platform is determined.With this approach,the multi-body dynamics of the electrical Stewart platform is better understood.