A novel modeling and control approach considering equality and inequality constraints based on generalized Udwadia-Kalaba equation

There are two categories of constraints for mechanical systems: equality and inequality. For the constrained mechanical systems with equality constraints, the Udwadia-Kalaba (U-K) equation can be used to model and introduce the constraint-following motion control method. In industrial automation and robotics, the problem of motion requirement with fixed boundary which is respond to an inequality constraint has not been solved systematically using constraint following method. Through transformation via a novel diffeomorphism, the equation of motion for a constrained mechanical system which addresses both equality and inequality constraints is presented. This can be considered a generalization of the Udwadia-Kalaba (U-K) equation. The advantages of the equation include that it does not require additional pseudo variables and the solution is analytical. This exhibits profound applications. As a demonstration, a pan/tilt device mounted under the firefighting unmanned aerial vehicles (UAVs) is manipulated. The water-jet nozzle need motion requirements of swaying horizontally and not overshooting limits in vertical. Simulation and experimental results are presented to validate the effectiveness of the proposed approach.