## Control of Forward Velocity for a Simplified Planar Hopping Robot (1995)

Venue: | Proc. 1995 IEEE Int. Conference on Robotics & Automation |

Citations: | 20 - 5 self |

### BibTeX

@INPROCEEDINGS{Schwind95controlof,

author = {William J. Schwind and Daniel E. Koditschek},

title = {Control of Forward Velocity for a Simplified Planar Hopping Robot},

booktitle = {Proc. 1995 IEEE Int. Conference on Robotics & Automation},

year = {1995},

pages = {691--696}

}

### OpenURL

### Abstract

A simplified lossless model of the Raibert planar hopper is introduced for the purpose of analytically studying the control of forward velocity. A closed-form return map describing the robot's state at the next hop as a function of that at the current hop is derived. The Raibert forward velocity controller is introduced and the fixed points of the closed loop system are characterized as well as the stability of these points. A new control law inspired by this analysis is introduced and compared with the Raibert control law. 1 Introduction This paper concerns the behavior of a planar hopping robot where the only control exerted is the placement of the leg at touchdown. This work is motivated by the dramatic success achieved by Marc Raibert in implementing simple control strategies to control physical hopping robots [5]. Raibert and his students built and studied hopping robots as a means to understand dynamic legged locomotion [5]. The first hopper was constrained to move in the plan...

### Citations

1537 |
Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (corrected 3rd printing
- Guckenheimer, Holmes
- 1990
(Show Context)
Citation Context ...cally the set of fixed points. This is easily verified, since the center eigenspace, i.e. that corresponding to the unity eigenvalue, is orthogonal to Dz fl and hence tangent to the fixed point curve =-=[1]-=-. Moreover, locally for points in FP S the transverse dynamics are converging towards the center manifold [6]. The attracting portion, FP S , of the fixed point curve is bounded by the condition \Gamm... |

525 |
Legged robots that balance
- Raibert
- 1986
(Show Context)
Citation Context ... exerted is the placement of the leg at touchdown. This work is motivated by the dramatic success achieved by Marc Raibert in implementing simple control strategies to control physical hopping robots =-=[5]-=-. Raibert and his students built and studied hopping robots as a means to understand dynamic legged locomotion [5]. The first hopper was constrained to move in the plane. It had a pneumatic cylinder f... |

90 |
Analysis of a Simplified Hopping Robot
- Koditschek, Buhler
- 1992
(Show Context)
Citation Context ...t by the National Science Foundation under grant IRI-9123266 a controller design validates the decoupling assumption. Previous work has endeavored to understand the control of vertical hopping height =-=[3]-=- [8] [7] and how it is influenced by the addition of the forward running dynamics [4]. In this paper, we restrict attention to the control of forward velocity. Specifically, this is accomplished by de... |

27 |
Periodic motions of a hopping robot with vertical and forward motion
- Mâ€™Closkey, Burdick
- 1993
(Show Context)
Citation Context ...dates the decoupling assumption. Previous work has endeavored to understand the control of vertical hopping height [3] [8] [7] and how it is influenced by the addition of the forward running dynamics =-=[4]-=-. In this paper, we restrict attention to the control of forward velocity. Specifically, this is accomplished by deriving a return map for a simplifed version of the Raibert planar hopper, wherein we ... |

19 |
DSTool: Dynamical System Toolkit with an Interactive Graphical Interface
- Guckenheimer, Meyers, et al.
- 1991
(Show Context)
Citation Context ...closed loop return map f u with the control law described above has been simulated using dstool, a dynamical systems simulation package designed by Guckenheimer and his students at Cornell University =-=[2]-=-. Using this package we generate the fixed points of the return map and then launch the system from a variety of initial conditions to obtain a rough picture of the domain of attraction of the stable ... |

18 |
An `interesting' strange attractor in the dynamics of a hopping robot
- Vakakis, Burdick, et al.
- 1991
(Show Context)
Citation Context ... the National Science Foundation under grant IRI-9123266 a controller design validates the decoupling assumption. Previous work has endeavored to understand the control of vertical hopping height [3] =-=[8]-=- [7] and how it is influenced by the addition of the forward running dynamics [4]. In this paper, we restrict attention to the control of forward velocity. Specifically, this is accomplished by derivi... |

2 | Analysis of a Hopping Robot. Paper submitted in fulfillment of research requirement for EECS - Schwind, Yoon - 1993 |