Abstract
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions, the second-order needle variations of optimal control, as the basis for choosing each control response to the current state. A second result of this paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Finally, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1826-1853 |
| Number of pages | 28 |
| Journal | International Journal of Robotics Research |
| Volume | 37 |
| Issue number | 13-14 |
| DOIs | |
| State | Published - Dec 1 2018 |
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article:This work was supported by the Office of Naval Research (grant number ONR N00014-14-1-0594) and by the National Science Foundation (grant number NSF CMMI 1662233). Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the Office of Naval Research or the National Science Foundation.
Keywords
- dynamics
- kinematics
- motion control
- underactuated robots
ASJC Scopus subject areas
- Software
- Modeling and Simulation
- Mechanical Engineering
- Electrical and Electronic Engineering
- Artificial Intelligence
- Applied Mathematics