Parameter Identification for Rigid Robot Models

A general overview of the identification methods of parameter for rigid robots can be found in textbooks. The identification techniques of experimental robot estimate dynamic robot parameters based on force/torque and motion data that are measured during robot motions along optimized trajectories. Mostly, these techniques are based on the fact that the dynamic robot model can be written as a linear set of equations with the dynamic parameters as unknowns. A formulation of dynamic parameters such as this allows the use of linear estimation techniques that find the optimal parameter set in a global sense. However, not all parameters can be defined using these techniques since some of the parameters do not affect the dynamic response or affect the dynamic response in linear combinations with other parameters.

The null space is defined as the parameter space consisting parameter combinations that do not impact the dynamic response. Gautier, Khalil and Mayeda provide a set of rules based on the topology of the manipulator system to group the dependent inertia parameters and to form a minimal set of parameters that uniquely determine the dynamic response of the robot. In addition, the techniques of numerical like the QR decomposition or the Singular Value Decomposition can be used to find the set of minimal or base parameters.

Mostly the base parameter set obtained from a linear parameter fit is not guaranteed to be a physically meaningful solution. Waiboer suggest that the identified parameters become more physically convincing by choosing the null space in such a way that the estimated parameters match a priori given values in least squares sense. This needs an a priori estimation of the parameter values and a sufficiently accurate description of the null space, neither of which are trivial, in general. Mata force is a physical feasible solution by adding nonlinear constraints to the optimization problem. However, by adding nonlinear constraints to a linear problem gives a nonlinear optimization problem for which it is hard to find the global minimum.