Abstract
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions-the needle variations of optimal control-as the basis for choosing each control response to the current state. A second result of the 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. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.
| Original language | English (US) |
|---|---|
| Title of host publication | Robotics |
| Subtitle of host publication | Science and Systems XIII, RSS 2017 |
| Publisher | MIT Press Journals |
| Volume | 13 |
| ISBN (Electronic) | 9780992374730 |
| State | Published - Jan 1 2017 |
| Event | 2017 Robotics: Science and Systems, RSS 2017 - Cambridge, United States Duration: Jul 12 2017 → Jul 16 2017 |
Other
| Other | 2017 Robotics: Science and Systems, RSS 2017 |
|---|---|
| Country | United States |
| City | Cambridge |
| Period | 7/12/17 → 7/16/17 |
Fingerprint
ASJC Scopus subject areas
- Artificial Intelligence
- Control and Systems Engineering
- Electrical and Electronic Engineering
Cite this
}
Feedback synthesis for controllable underactuated systems using sequential second order actions. / Mamakoukas, Giorgos; MacIver, Malcolm A.; Murphey, Todd D.
Robotics: Science and Systems XIII, RSS 2017. Vol. 13 MIT Press Journals, 2017.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
TY - GEN
T1 - Feedback synthesis for controllable underactuated systems using sequential second order actions
AU - Mamakoukas, Giorgos
AU - MacIver, Malcolm A.
AU - Murphey, Todd D.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions-the needle variations of optimal control-as the basis for choosing each control response to the current state. A second result of the 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. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.
AB - This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions-the needle variations of optimal control-as the basis for choosing each control response to the current state. A second result of the 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. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.
UR - http://www.scopus.com/inward/record.url?scp=85048743590&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85048743590&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:85048743590
VL - 13
BT - Robotics
PB - MIT Press Journals
ER -