Uniform Complete Observability of Mass and Rotational Inertial Parameters in Adaptive Identification of Rigid-Body Plant Dynamics

• Main Authors: Paine, Tyler M, Whitcomb, Louis L
• Format: Journal Article
• Language: English
• Published: 09-12-2021
• Subjects: Computer Science - Robotics; Computer Science - Systems and Control
• DOI: 10.48550/arxiv.2108.05297

2021 IEEE International Conference on Robotics and Automation
(ICRA) This paper addresses the long-standing open problem of observability of mass
and inertia plant parameters in the adaptive identification (AID) of
second-order nonlinear models of 6 degree-of-freedom rigid-body dynamical
systems subject to externally applied forces and moments. Although stable
methods for AID of plant parameters for this class of systems, as well numerous
approaches to stable model-based direct adaptive trajectory-tracking control of
such systems, have been reported, these studies have been unable to prove
analytically that the adaptive parameter estimates converge to the true plant
parameter values. This paper reports necessary and sufficient conditions for
the uniform complete observability (UCO) of 6-DOF plant inertial parameters for
a stable adaptive identifier for this class of systems. When the UCO condition
is satisfied, the adaptive parameter estimates are shown to converge to the
true plant parameter values. To the best of our knowledge this is the first
reported proof for this class of systems of UCO of plant parameters and for
convergence of adaptive parameter estimates to true parameter values.
We also report a numerical simulation study of this AID approach which shows
that (a) the UCO condition can be met for fully-actuated plants as well as
underactuated plants with the proper choice of control input and (b)
convergence of adaptive parameter estimates to the true parameter values. We
conjecture that this approach can be extended to include other parameters that
appear rigid body plant models including parameters for drag, buoyancy, added
mass, bias, and actuators.