Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight

Abstract

This paper describes a fully decentralized nonlinear control law for spinning tethered formation flight, based on exploiting geometric symmetries to reduce the original nonlinear dynamics into simpler stable dynamics. Motivated by oscillation synchronization in biological systems, we use contraction theory to prove that a control law stabilizing a single-tethered spacecraft can also stabilize arbitrary large circular arrays of spacecraft, as well as the three inline configuration. The convergence result is global and exponential. Numerical simulations and experimental results using the SPHERES testbed validate the exponential stability of the tethered formation arrays by implementing a tracking control law derived from the reduced dynamics.

Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

“…The proposed tracking and synchronization control law in (8) can easily be applied to a network consisting of heterogeneous robots in (2) if the stable tracking condition in Theorem 6 is true.…”

“…3 represents the concurrent synchronization of two different dynamic networks. The first network, consisting of four heterogeneous robots, has the diffusive coupling structure proposed by the tracking control law in (8). The independent leader sends a desired trajectory command q d (t) to each member of the first network.…”

“…Consider the following adaptive control law [18], [40], [41] that has the same local coupling structure as the proposed control law in (8): (38) where s i =q i −q i,r . Also, the parameter estimateâ i for the ith member is updated by the correlation integral…”

“…In production processes, such as manufacturing and automotive applications, where high flexibility, manipulability, and maneuverability cannot be achieved by a single system [38], there has been widespread interest in cooperative schemes for multiple robot manipulators that track a predefined trajectory. A stellar formation flight interferometer [8], [9] is another example where precision control of relative spacecraft motions is indispensable. The proposed synchronization tracking control law can be implemented for such purposes, where a common desired trajectory can be explicitly given.…”

Propellant-Free Control of Tethered Formation Flight, Part 2: Nonlinear Underactuated Control

“…Most aforementioned work is restricted to a single-body dynamics problem. In this paper, the decentralized control strategy from out prior work 19 is extended to the underactuated control of multi-vehicle tethered formation flying. To our knowledge, this work presents the first linear and nonlinear control results for underactuated tethered formation flight systems.…”