Recursive Estimation of Orientation Based on the Bingham Distribution

Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly because they fail to take the periodic nature of the problem into account. We present a recursive filter for directional data based on the Bingham distribution in two dimensions. The proposed filter can be applied to circular filtering problems with 180 degree symmetry, i.e., rotations by 180 degrees cannot be distinguished. It is easily implemented using standard numerical techniques and suitable for real-time applications. The presented approach is extensible to quaternions, which allow tracking arbitrary three-dimensional orientations. We evaluate our filter in a challenging scenario and compare it to a traditional Kalman filtering approach

Unscented Orientation Estimation Based on the Bingham Distribution

Orientation estimation for 3D objects is a common problem that is usually tackled with traditional nonlinear filtering techniques such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). Most of these techniques assume Gaussian distributions to account for system noise and uncertain measurements. This distributional assumption does not consider the periodic nature of pose and orientation uncertainty. We propose a filter that considers the periodicity of the orientation estimation problem in its distributional assumption. This is achieved by making use of the Bingham distribution, which is defined on the hypersphere and thus inherently more suitable to periodic problems. Furthermore, handling of non-trivial system functions is done using deterministic sampling in an efficient way. A deterministic sampling scheme reminiscent of the UKF is proposed for the nonlinear manifold of orientations. It is the first deterministic sampling scheme that truly reflects the nonlinear manifold of the orientation

A surgical system for automatic registration, stiffness mapping and dynamic image overlay

In this paper we develop a surgical system using the da Vinci research kit (dVRK) that is capable of autonomously searching for tumors and dynamically displaying the tumor location using augmented reality. Such a system has the potential to quickly reveal the location and shape of tumors and visually overlay that information to reduce the cognitive overload of the surgeon. We believe that our approach is one of the first to incorporate state-of-the-art methods in registration, force sensing and tumor localization into a unified surgical system. First, the preoperative model is registered to the intra-operative scene using a Bingham distribution-based filtering approach. An active level set estimation is then used to find the location and the shape of the tumors. We use a recently developed miniature force sensor to perform the palpation. The estimated stiffness map is then dynamically overlaid onto the registered preoperative model of the organ. We demonstrate the efficacy of our system by performing experiments on phantom prostate models with embedded stiff inclusions.Comment: International Symposium on Medical Robotics (ISMR 2018

Online Estimation of Self-Body Deflection With Various Sensor Data Based on Directional Statistics

In this paper, we propose a method for online estimation of the robot's posture. Our method uses von Mises and Bingham distributions as probability distributions of joint angles and 3D orientation, which are used in directional statistics. We constructed a particle filter using these distributions and configured a system to estimate the robot's posture from various sensor information (e.g., joint encoders, IMU sensors, and cameras). Furthermore, unlike tangent space approximations, these distributions can handle global features and represent sensor characteristics as observation noises. As an application, we show that the yaw drift of a 6-axis IMU sensor can be represented probabilistically to prevent adverse effects on attitude estimation. For the estimation, we used an approximate model that assumes the actual robot posture can be reproduced by correcting the joint angles of a rigid body model. In the experiment part, we tested the estimator's effectiveness by examining that the joint angles generated with the approximate model can be estimated using the link pose of the same model. We then applied the estimator to the actual robot and confirmed that the gripper position could be estimated, thereby verifying the validity of the approximate model in our situation.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl