Rangaprasad Arun Srivatsan

Complementary model update: A method for simultaneous registration and stiffness mapping in flexible environments

Registering a surgical tool to an a priori model of the environment is an important first step in computer-aided surgery. In this paper we present an approach for simultaneous registration and stiffness mapping using blind exploration of flexible environments. During contact-based exploration of flexible environments, the physical interaction with the environment can induce local deformation, leading to erroneous registration if not accounted for. To overcome this issue, a new registration method called complementary model update (CMU), is introduced. By incorporating measurements of the contact force, and contact location, we minimize a unique objective function to cancel out the effect of local deformation. We are thus able to acquire the necessary registration parameters using both geometry and stiffness information. The proposed CMU method is evaluated in simulation and using experimental data obtained by probing silicone models and an ex vivo organ.

Using Bayesian optimization to guide probing of a flexible environment for simultaneous registration and stiffness mapping

One of the goals of computer-aided surgery is to register intraoperative data to preoperative model of the anatomy, and hence add complementary information that can facilitate the task of surgical navigation. In this context, mechanical palpation can reveal critical anatomical features such as arteries and cancerous lumps which are stiffer than the surrounding tissue. This work uses position and force measurements obtained during mechanical palpation for registration and stiffness mapping. Prior approaches, including our own, exhaustively palpated the entire organ to achieve this goal. To overcome the costly palpation of the entire organ, a Bayesian optimization framework is introduced to guide the end effector to palpate stiff regions while simultaneously updating the registration of the end effector to an a priori geometric model of the organ, hence enabling the fusion of intraoperative data into the a priori model obtained through imaging. This new framework uses Gaussian processes to model the stiffness distribution and Bayesian optimization to direct where to sample next for maximum information gain. The proposed method was evaluated with experimental data obtained using a Cartesian robot interacting with a silicone organ model and an ex vivo porcine liver.

Using Lie algebra for shape estimation of medical snake robots

Highly articulated robots have the potential to play a key role in minimally invasive surgeries by providing improved access to hard-to-reach anatomy. Estimating their shape inside the body and combining it with 3D preoperative scans of the anatomy enable the surgeon to visualize how the entire robot interacts with the internal organs. As the robot progresses inside the body, the position and orientation of every link comprising the robot, evolves over a coordinate-free Lie algebra, se(3). To capture the full motion and uncertainty of the system, we use an extended Kalman filter where the state vector is defined using elements of se(3). We show that this approach describes the shape of the robot more accurately, than the ones where the state vector is a conventional parametrization, such as Cartesian coordinates and Euler angles. We perform two experiments to demonstrate the effectiveness of this new filtering approach.

Analysis of Constraint Equations and Their Singularities

The identification of singularities is an important aspect of research in parallel manipulators, which has received a great deal of attention in the past few decades. Yet, even in many well-studied manipulators, very few reported results are of complete or analytical nature. This chapter tries to address this issue from a slightly different perspective than the standard method of Jacobian analysis. Using the condition for existence of repeated roots of the univariate equation representing the forward kinematic problem of the manipulator, it shows that it is possible to gain some more analytical insight into such problems. The proposed notions are illustrated by means of applications to a spatial \(3\)-RPS manipulator, leading to the closed-form expressions for the singularity manifold of the \(3\)-RPS in the actuator space.

Estimating SE(3) elements using a dual quaternion based linear Kalman filter.

Many applications in robotics such as registration, object tracking, sensor calibration, etc. use Kalman filters to estimate a time invariant SE(3) element by locally linearizing a non-linear measurement model. Linearization-based filters tend to suffer from inaccurate estimates, and in some cases divergence, in the presence of large initialization errors. In this work, we use a dual quaternion to represent the SE(3) element and use multiple measurements simultaneously to rewrite the measurement model in a truly linear form with state dependent measurement noise. Use of the linear measurement model bypasses the need for any linearization in prescribing the Kalman filter, resulting in accurate estimates while being less sensitive to initial estimation error. To show the broad applicability of this approach, we derive linear measurement models for applications that use either position measurements or pose measurements. A procedure to estimate the state dependent measurement uncertainty is also discussed. The efficacy of the formulation is illustrated using simulations and hardware experiments for two applications in robotics: rigid registration and sensor calibration.

Probabilistic pose estimation using a Bingham distribution-based linear filter

Pose estimation is central to several robotics applications such as registration, hand–eye calibration, and simultaneous localization and mapping (SLAM). Online pose estimation methods typically use Gaussian distributions to describe the uncertainty in the pose parameters. Such a description can be inadequate when using parameters such as unit quaternions that are not unimodally distributed. A Bingham distribution can effectively model the uncertainty in unit quaternions, as it has antipodal symmetry, and is defined on a unit hypersphere. A combination of Gaussian and Bingham distributions is used to develop a truly linear filter that accurately estimates the distribution of the pose parameters. The linear filter, however, comes at the cost of state-dependent measurement uncertainty. Using results from stochastic theory, we show that the state-dependent measurement uncertainty can be evaluated exactly. To show the broad applicability of this approach, we derive linear measurement models for applications that use position, surface-normal, and pose measurements. Experiments assert that this approach is robust to initial estimation errors as well as sensor noise. Compared with state-of-the-art methods, our approach takes fewer iterations to converge onto the correct pose estimate. The efficacy of the formulation is illustrated with a number of examples on standard datasets as well as real-world experiments.