## Collision-free state estimation (2012)

Venue: | IN ICRA |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Wong12collision-freestate,

author = {Lawson L. S. Wong and Leslie Pack Kaelbling and Tomás Lozano-Pérez},

title = {Collision-free state estimation},

booktitle = {IN ICRA},

year = {2012},

publisher = {}

}

### OpenURL

### Abstract

In state estimation, we often want the maximum likelihood estimate of the current state. For the commonly used joint multivariate Gaussian distribution over the state space, this can be efficiently found using a Kalman filter. However, in complex environments the state space is often highly constrained. For example, for objects within a refrigerator, they cannot interpenetrate each other or the refrigerator walls. The multivariate Gaussian is unconstrained over the state space and cannot incorporate these constraints. In particular, the state estimate returned by the unconstrained distribution may itself be infeasible. Instead, we solve a related constrained optimization problem to find a good feasible state estimate. We illustrate this for estimating collision-free configurations for objects resting stably on a 2-D surface, and demonstrate its utility in a real robot perception domain.

### Citations

42 |
Kalman filtering with state equality constraints
- Simon, Chia
(Show Context)
Citation Context ...monstrate its utility in a real robot perception domain. A. Related Work There has been considerable interest in general constrained state estimation, particularly in the context of Kalman filtering (=-=[1]-=-, [2], [3], [4]). These works mainly focus on linear state equalities and inequalities; nonlinear constraints have been considered with linearization techniques. A survey of such techniques is given b... |

40 | Approximate bayesian multibody tracking
- Lanz
(Show Context)
Citation Context ...endencies has been of particular interest to the multi-target tracking and data association community, where explicitly modeling correlations and occlusions is useful. Recent methods such as [11] and =-=[12]-=- typically derive a complex measurement model, then use particle methods to handle the otherwise intractable filter. Much of the complexity in these techniques however is devoted to data association p... |

25 | Multitarget tracking using the joint multitarget probability density
- Kreucher, Kastella, et al.
(Show Context)
Citation Context ...state dependencies has been of particular interest to the multi-target tracking and data association community, where explicitly modeling correlations and occlusions is useful. Recent methods such as =-=[11]-=- and [12] typically derive a complex measurement model, then use particle methods to handle the otherwise intractable filter. Much of the complexity in these techniques however is devoted to data asso... |

17 | Kalman filtering with state constrains: a survey of linear and nonlinear algorithms
- Simon, Chia
- 2010
(Show Context)
Citation Context ...3], [4]). These works mainly focus on linear state equalities and inequalities; nonlinear constraints have been considered with linearization techniques. A survey of such techniques is given by Simon =-=[5]-=-. The main result from many of these works is that constrained state estimation can be performed reasonably well by filtering as in the unconstrained case, and projecting the solution back to the stat... |

9 |
Constrained Kalman filtering via density function truncation for turbofan engine health estimation
- Simon, Simon
(Show Context)
Citation Context ...ore concerned with how to perform this projection step. In previous work, constraints in practice have been upper/lower bounds on various physical state quantities, for example aircraft engine health =-=[6]-=-, odometry [7], road boundaries when tracking a car [8], acceleration of a moving object [9]. Our current problem constrains object configurations to be collision-free. To our knowledge, this type of ... |

5 |
Some Results on the Multivariate Truncated Normal Distribution
- Horrace
- 2001
(Show Context)
Citation Context ...region, the posterior density will therefore have Gaussian shape over the feasible region, and zero otherwise. This posterior distribution is similar to a multivariate truncated Gaussian distribution =-=[13]-=-, in the sense that it has Gaussian shape over some constrained region. However, truncated Gaussians only have upper and lower bounds on their parameters, whereas in our case the collision constraints... |

4 | Kalman Filtering with Equality and Inequality State Constraints’, http://arxiv.org/abs/0709.2791, 2007, accessed
- Gupta, Hauser
- 2009
(Show Context)
Citation Context ...rate its utility in a real robot perception domain. A. Related Work There has been considerable interest in general constrained state estimation, particularly in the context of Kalman filtering ([1], =-=[2]-=-, [3], [4]). These works mainly focus on linear state equalities and inequalities; nonlinear constraints have been considered with linearization techniques. A survey of such techniques is given by Sim... |

4 | Monte carlo pose estimation with quaternion kernels and the bingham distribution
- Glover, Bradsky, et al.
- 2011
(Show Context)
Citation Context ... arise. be done efficiently in 2-D, and are modeled with simple polygonal shapes. We used a Willow Garage PR2 robot platform to perform perception tasks, and for pose estimation we used the method in =-=[14]-=- (using stereo camera data only). To solve the optimization problem (4), the SQP solver in the MATLAB Optimization Toolbox was used. Collision checking between object pairs was performed by computing ... |

3 |
State Estimation for Linear and Non-linear Equality-constrained Systems
- Teixeira, Chandrasekar, et al.
- 2009
(Show Context)
Citation Context ...its utility in a real robot perception domain. A. Related Work There has been considerable interest in general constrained state estimation, particularly in the context of Kalman filtering ([1], [2], =-=[3]-=-, [4]). These works mainly focus on linear state equalities and inequalities; nonlinear constraints have been considered with linearization techniques. A survey of such techniques is given by Simon [5... |

2 |
Constrained Kalman filter for mobile robot localization with gyroscope
- Myung, Lee, et al.
- 2006
(Show Context)
Citation Context ...with how to perform this projection step. In previous work, constraints in practice have been upper/lower bounds on various physical state quantities, for example aircraft engine health [6], odometry =-=[7]-=-, road boundaries when tracking a car [8], acceleration of a moving object [9]. Our current problem constrains object configurations to be collision-free. To our knowledge, this type of constraint has... |

2 | State estimation under nonlinear state inequality constraints. A tracking application
- Sircoulomb, Israel, et al.
- 2008
(Show Context)
Citation Context ...ctice have been upper/lower bounds on various physical state quantities, for example aircraft engine health [6], odometry [7], road boundaries when tracking a car [8], acceleration of a moving object =-=[9]-=-. Our current problem constrains object configurations to be collision-free. To our knowledge, this type of constraint has not been previously considered within the context of Kalman filtering. Partic... |

1 |
Dynamic estimation of linear systems constrained by bounds
- Monin
- 2009
(Show Context)
Citation Context ...tility in a real robot perception domain. A. Related Work There has been considerable interest in general constrained state estimation, particularly in the context of Kalman filtering ([1], [2], [3], =-=[4]-=-). These works mainly focus on linear state equalities and inequalities; nonlinear constraints have been considered with linearization techniques. A survey of such techniques is given by Simon [5]. Th... |

1 |
Estimation and filtering of Gaussian variables with linear inequality constraints
- Xu, Li
- 2010
(Show Context)
Citation Context ... In previous work, constraints in practice have been upper/lower bounds on various physical state quantities, for example aircraft engine health [6], odometry [7], road boundaries when tracking a car =-=[8]-=-, acceleration of a moving object [9]. Our current problem constrains object configurations to be collision-free. To our knowledge, this type of constraint has not been previously considered within th... |

1 | Probabilistic rule set joint state update as approximation to the full joint state estimation applied to multi object scene analysis
- Grundmann, Fiegert, et al.
- 2010
(Show Context)
Citation Context ...ernative for tracking complex, non-Gaussian states. However, they suffer from the curse of dimensionality and become computationally intractable in high dimensions. To mitigate this, Grundmann et al. =-=[10]-=- used a particle filter that first updated object states separately, then evaluated the joint estimates using a rule set. The rule set encoded physical constraints such as non-interpenetration and gra... |