Inversion-based nonlinear control of robot arms with flexible links

Alessandro De Luca, Bruno Siciliano
1993 Journal of Guidance Control and Dynamics  
The design of inversion-based nonlinear control laws solving the problem of accurate trajectory tracking for robot arms having flexible links is considered. It is shown that smooth joint trajectories can always be exactly reproduced preserving internal stability of the closed-loop system. The interaction between the Lagrangian/assumed modes modeling approach and the complexity of the resulting inversion control laws is stressed. The adoption of clamped boundary conditions at the actuation side
more » ... f the flexible links allows considerable simplification with respect to the case of pinned boundary conditions. The resulting control is composed of a nonlinear state feedback compensation term and of a linear feedback stabilization term. A feedforward strategy for the nonlinear part is also investigated. Simulation results are presented for a planar manipulator with two flexible links, displaying the performance of the proposed controllers also in terms of end-effector behavior. a s dd See T t u "des Ur V Wj Xi Nomenclature = system matrices in closed-loop flexible dynamics = acceleration input vector = sub-blocks of inertia matrix = modal damping matrix = /th link flexural rigidity = input matrix in modified rigid dynamics = jth natural frequency of /th link : Coriolis and centrifugal force vectors = identity matrix = /th hub inertia = /th link inertia about relative joint axis = tip payload inertia = modal stiffness matrix = derivative feedback gain matrix = proportional feedback gain matrix = /th link length = number of deflection variables = /th hub mass = /th link mass = tip payload mass = number of joint variables = compound vector in flexible dynamics = null matrix = input weighting matrix = factorization matrix for h 5 • • factorization matrix for h e • trajectory traveling time = time = input torque = feedforward input torque = computed torque for modified rigid dynamics = Lyapunov function = /th link deflection = position along /th link d <$des Pi = vector of deflection variables = vector of desired deflection variables = yth modal coefficient of /th link = vector of initial deflection variables = vector of joint variables = vector of desired joint variables = /th joint variable = number of modes of /th link = /th link density = yth mode shape of /th link = forcing vector term in closed-loop flexible dynamics Superscripts T -1 = matrix (vector) transpose = matrix inverse = spatial derivative = time derivative = estimate
doi:10.2514/3.21142 fatcat:b3dgtlucjnaghhapkkefv67xau