On the inseparable nature of sensor selection, sensor placement, and state estimation for continuum robots or “where to put your sensors and how to use them”

Abstract

When designing continuum robots for applications that require sensing, designers are faced with the problems of deciding what sensors to use, where they should be placed, and how best to use the information they provide. In this paper, we describe how a differential representation of a continuum robot's kinematic equations that govern its states (e.g., shape) can be used to simultaneously address these problems under the guidance of statistical state estimation. We identify how state estimation and sensing-system design (i.e., sensor selection and placement) are inherently coupled problems, which leads us to formulate sensing-system design as an optimization problem governed by the results of statistical estimation. As a case-study, the methods described herein are used to design a magnetic sensing system for concentric-tube robots.

Continuum Reconfigurable Parallel Robots for Surgery: Shape Sensing and State Estimation With Uncertainty

“…3(b) also illustrates that some CRISP configurations are more information-rich than others (this was also observed for concentric-tube continuum robots [17]). When selecting how a CRISP system should be reconfigured to meet changing application requirements, the system covariance will be an important consideration.…”

“…After the requirements for observability are ensured, the smoothed covariance matrix ${\overline{P}}_s$ can be used to reduce the uncertainty of a CRISP system’s state estimates. A task-specific covariance-based metric is introduced for this purpose in [17]. This ultimately turns the problem of selecting where to place sensor observations into an optimization problem.…”

“…Clinically relevant sensors include electromagnetic tracking sensors [14], optical tracking systems [15], and fiber Bragg-grating (FBG) sensors [16]. In the remainder of this paper we extend concepts originally developed for continuum robots in [17] to CRISP systems that enable powerful classical estimation techniques to be used to reason about a CRISP system’s state in the presence of uncertainty.…”

Highly dexterous 2‐module soft robot for intra‐organ navigation in minimally invasive surgery

“…Definition of the kinematics allows a direct mapping between the actuator states, or the lengths of the actuators, and the coordinate space position of the end effector, removing the influences of the sensors themselves. It also enables simulation of the capabilities of the robot and ultimately effective control of it, without the use of position sensors, which may influence the soft robot performances . Based on the design of the module and for the sake of simplification, the kinematics are based on the constant curvature (CC) assumption .…”

“…It also enables simulation of the capabilities of the robot and ultimately effective control of it, without the use of position sensors, 24,29 which may influence the soft robot performances. [30][31][32] Based on the design of the module and for the sake of simplification, the kinematics are based on the constant curvature (CC) assumption. 33 The kinematics mapping can be broken into two parts, one from the states of the robot (length of chambers in this case) to arc parameters and the other from the arc parameters to the position of the robot in the coordinate system.…”