## Controllability of a Planar Body with Unilateral Thrusters (1999)

Venue: | IEEE Trans. on Automatic Control |

Citations: | 12 - 6 self |

### BibTeX

@ARTICLE{Lynch99controllabilityof,

author = {Kevin M. Lynch},

title = {Controllability of a Planar Body with Unilateral Thrusters},

journal = {IEEE Trans. on Automatic Control},

year = {1999},

volume = {44},

pages = {1206--1211}

}

### OpenURL

### Abstract

This note investigates the minimal number of unilateral thrusters required for different versions of nonlinear controllability of a planar rigid body. For one to three unilateral thrusters, we get a new property with each additional thruster: one thruster yields small-time accessibility on the body's state space TSE(2); two thrusters yield global controllability on TSE(2); and three thrusters yield small-time local controllability at zero velocity states.

### Citations

268 |
der Schaft. Nonlinear Dynamical Control Systems
- Nijmeijer, van
- 1990
(Show Context)
Citation Context ... 1) andsi is the torque about the center of mass. We will write f i = (f xi ; f yi ;si ) T , where (f xi ; f yi ) is the linear component of f i . Modifying notation from Nijmeijer and van der Schaft =-=[8]-=-, we define R V (q 0 ;sq 0 ; T ) to be the reachable set from (q 0 ;sq 0 ) at time T ? 0 by feasible trajectories remaining in the neighborhood V of (q 0 ;sq 0 ) at times t 2 [0; T ]. Define R V (q 0 ... |

155 |
Nonlinear controllability and observability
- Hermann, Krener
- 1977
(Show Context)
Citation Context ...ctors of L(V) at p are L(V)(p). Then the system satisfies the Lie Algebra Rank Condition at p, and therefore is small-time accessible from p, if L(V)(p) is the tangent space T p M (Hermann and Krener =-=[2]-=-; Sussmann [10]). Note that V need not be symmetric for small-time accessibility; in particular, if V is an element of V, it is not necessary that \GammaV also belong to V. For the case n = 1 we study... |

120 |
A general theorem on local controllability
- Sussmann
- 1987
(Show Context)
Citation Context ...at p are L(V)(p). Then the system satisfies the Lie Algebra Rank Condition at p, and therefore is small-time accessible from p, if L(V)(p) is the tangent space T p M (Hermann and Krener [2]; Sussmann =-=[10]-=-). Note that V need not be symmetric for small-time accessibility; in particular, if V is an element of V, it is not necessary that \GammaV also belong to V. For the case n = 1 we study the Lie algebr... |

112 |
Stable pushing: Mechanics, controllability, and planning
- Lynch, Mason
- 1995
(Show Context)
Citation Context ...d hence not small-time locally controllable. Our interest in unilateral control forces arises from our previous work on robotic pushing of an object over a frictional support surface (Lynch and Mason =-=[5]-=-) and dynamic nonprehensile manipulation (Lynch and Mason [6]). In both cases, the robot controls the motion of an object by applying forces through unilateral contact. Unilateral inputs are fundament... |

70 | Configuration controllability of simple mechanical control systems
- Lewis, Murray
- 1999
(Show Context)
Citation Context ...nlinear controllability of a planar rigid body. The dynamics can be viewed as a simple model of a planar spacecraft or hovercraft, also studied by Manikonda and Krishnaprasad [7] and Lewis and Murray =-=[4]-=-. The configuration space of the body is C = SE(2), the set of planar positions and orientations, and its state space is the tangent bundle TC. The configuration of the planar body is q and its state ... |

32 | Dynamic nonprehensile manipulation: Controllability, planning and experiments
- Lynch, Mason
- 1999
(Show Context)
Citation Context ...unilateral control forces arises from our previous work on robotic pushing of an object over a frictional support surface (Lynch and Mason [5]) and dynamic nonprehensile manipulation (Lynch and Mason =-=[6]-=-). In both cases, the robot controls the motion of an object by applying forces through unilateral contact. Unilateral inputs are fundamental to the controllability analyses of these systems, and the ... |

21 |
A sufficient condition for local controllability
- Sussmann
- 1978
(Show Context)
Citation Context ...ce (f x ; f y ;s). Therefore the tangent vectors X 1 (q;sq) and X 2 (q;sq) are confined to an open halfspace of T (q;sq) TC at any state (q;sq), and B is not small-time locally controllable (Sussmann =-=[9]-=-). 9 6 Three Thrusters Under certain conditions, the Lie Algebra Rank Condition can be used to prove small-time local controllability. One such condition is that the system vector fields are symmetric... |

15 |
1997] Local configuration controllability for a class of mechanical systems with a single input
- Lewis
(Show Context)
Citation Context ...full state space, not just the configuration space.) They showed that a planar body with two bilateral thrusters (or four unilateral thrusters) is small-time locally configuration controllable. Lewis =-=[3]-=- also showed that a planar body with a single bilateral thruster is not small-time locally configuration controllable, and hence not small-time locally controllable. Our interest in unilateral control... |

11 | Controllability of Lie-Poisson reduced dynamics
- Manikonda, Krishnaprasad
- 1997
(Show Context)
Citation Context ... different versions of nonlinear controllability of a planar rigid body. The dynamics can be viewed as a simple model of a planar spacecraft or hovercraft, also studied by Manikonda and Krishnaprasad =-=[7]-=- and Lewis and Murray [4]. The configuration space of the body is C = SE(2), the set of planar positions and orientations, and its state space is the tangent bundle TC. The configuration of the planar... |

9 | Controllability with unilateral control inputs
- Goodwine, Burdick
- 1996
(Show Context)
Citation Context ... can never be small-time locally controllable. These properties are also tight if we relax restrictions 3 and 4 on the thrusters, allowing simultaneous use of multiple thrusters with thrust values in =-=[0; 1]-=-. 2 Definitions A coordinate frame F B is attached to the center of mass of the planar body B, and its configuration in an inertial frame FW is given by q = (xw ; yw ; ` w ) T . The state of B is writ... |