Dual Quaternion Particle Filtering for Pose Estimation

Abstract

This article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodrigues parameters (MRPs) are used for local pose representation in the state-space model. The dual MRPs enable estimates of the mean and the covariance to be calculated from the particles without violating the algebraic constraint of the unit dual quaternion. For verification of the filter and comparison with state of the art, we consider pose measurements available in the form of unit dual quaternions. Angular velocity and specific force measurements from a body-mounted inertial measurement unit are also considered in the filtering. We show through simulations that the suggested particle filter has comparable accuracy with a previously proposed unscented Kalman filter based on unit dual quaternions. We also consider a practical application where the pose of an arbitrary rigid object is estimated using a sequence of point clouds from a 3-D camera. A model point cloud of the object is displaced with the unit dual quaternion associated with each particle, and a fitting score is calculated between the displaced model point cloud and the measured point cloud from the 3-D camera. The likelihoods of the fitting scores are calculated from an exponential distribution and are used to update the weights of the particles. The system was verified in an experiment where the motion of a swinging payload hanging from a crane was estimated using a 3-D camera.

Pose Estimation based on a Dual Quaternion Feedback Particle Filter

“…In this section, we apply our approach on point registration scenarios on both known and unknown corresponding cases. The performance is studied as follows, where the Kalman filter-based method (DQKF) [21], Bingham filterbased method (BMF) [7], and a modified particle filterbased method (DQPF) [19] are taken as the baseline for comparison 4 .…”

“…Likewise, K.Fathian et al [18] presented an iterative extended Kalman filter to optimize the nonlinear model. Considering the representation of the pose, Aksel et al [19] presented a dual quaternion particle filter for online pose estimation since dual quaternions can accurately represent both rotations and translations. Kaikai et al [20] proposed to utilize a dual quaternion unscented Kalman filter combined with the particle filter to estimate the pose.…”

A Review on the Applications of Dual Quaternions

“…Simultaneous Localization and Mapping, also known as SLAM [113,114], uses a mobile robot's onboard sensors to make sense of its surroundings, building a map as it moves. Pose Estimation is also treated using dual quaternions using Moving Horizon Estimator [115], 6-DOF observer [98] and Particle Filter [116]. In formation control [92,117], using dual quaternions [118] provides a controller for a formation consisting of a ground vehicle being escorted by an aerial one.…”

DPO: Direct Planar Odometry with Stereo Camera

“…In addition, they offer the most compact way to represent rotations and translations. More recently, they have been employed in visual SLAM techniques based on stochastic filters [ 40 , 41 , 42 , 43 , 44 , 45 ], and some based on graph-SLAM [ 46 , 47 ] have been observed. Despite the wide use of this parametrization in feature-based SLAM approaches, our approach is the first to use it in direct VO.…”