Dynamic equations are developed in nonrecursive symbolic form for chain-structured robotic manipulators with compliant links. A program is developed in REDUCE to automate the symbolic expansion of these equations for any given chain-structured manipulator. The symbolic nonrecursive form of the dynamic model is particularly suitable for controller synthesis and real-time control implementations.>

A lattice-filter structure is used for real-time parameter estimation of a flexible one-arm robot. The estimated parameters are employed in the control calculations based on predictive adaptive output feedback control. The lattice filters are particularly suitable for identifying the parameters of mechanical systems with distributed flexibility, since the order of the filter may be adjusted online as the task conditions require. Hence, the required dynamic model order for an accurate control does not have to be decided upon beforehand. A predictive adaptive control is studied using tip-position measurements. Although there are potential instability problems due to the nonminimum-phase nature of the open-loop system as a result of sensor-actuator noncolocation, the discrete-time predictive adaptive control implemented with the lattice filter (forming a special self-tuning regulator) demonstrated precision, high-bandwidth tip-position control of a flexible one-arm robot.>

The performance limitations of manipulators under joint variable-feedback control are studied as a function of the mechanical flexibility inherent in the manipulator structure. A finite-dimensional time-domain dynamic model of a two-link, two-joint planar manipulator is used in the study. Emphasis is placed on determining the limitations of control algorithms that use only joint variable-feedback information in calculations of control decisions, since most motion control systems in practice are of this kind. Both fine and gross motion cases are studied. Results for fine motion agree well with previously reported results in the literature and are also helpful in explaining the performance limitations in fast gross motions.>

This paper presents a new systematic algorithm to symbolically derive the full nonlinear dynamic equations of motion of multi-link flexible manipulators. Lagrange's-Assumed modes method is the basis of the new algorithm and adapted in a way suitable for symbolic manipulation by digital computers. It is applied to model a two-link flexible arm via a commercially available symbolic manipulation program. The advantages of the algorithm and simulation results are discussed.