Continuum robot state estimation using Gaussian process regression on SE(3)

Abstract

Continuum robots have the potential to enable new applications in medicine, inspection, and countless other areas due to their unique shape, compliance, and size. Excellent progress has been made in the mechanical design and dynamic modeling of continuum robots, to the point that there are some canonical designs, although new concepts continue to be explored. In this paper, we turn to the problem of state estimation for continuum robots that can been modeled with the common Cosserat rod model. Sensing for continuum robots might comprise external camera observations, embedded tracking coils, or strain gauges. We repurpose a Gaussian process (GP) regression approach to state estimation, initially developed for continuous-time trajectory estimation in SE(3). In our case, the continuous variable is not time but arclength and we show how to estimate the continuous shape (and strain) of the robot (along with associated uncertainties) given discrete, noisy measurements of both pose and strain along the length. We demonstrate our approach quantitatively through simulations as well as through experiments. Our evaluations show that accurate and continuous estimates of a continuum robot’s shape can be achieved, resulting in average end-effector errors between the estimated and ground truth shape as low as 3.5 mm and 0.016° in simulation or 3.3 mm and 0.035° for unloaded configurations and 6.2 mm and 0.041° for loaded ones during experiments, when using discrete pose measurements.

An Efficient Multi-solution Solver for the Inverse Kinematics of 3-Section Constant-Curvature Robots

“…In order to better manoeuvre a particular continuum manipulator, the strategy employed for modelling the kinematics is essential, concerning the mechanical design, material properties and geometrical characteristics. It is also indispensable for fitting sensor observation [19] or state estimation [20]. Three popular techniques of modelling include (1) The piecewise constant curvature model (see Webster III and Jones [21] for a review), (2) The Cosserat rod model [22,23,24], and (3) The finite element model [25].…”

“…Three popular techniques of modelling include (1) The piecewise constant curvature model (see Webster III and Jones [21] for a review), (2) The Cosserat rod model [22,23,24], and (3) The finite element model [25]. Among them, the piecewise constant curvature model is perhaps the most well-known and widely used kinematic framework for continuum robots [7,20,26]. In practice, many tasks such as motion planning [11] and trajectory tracking [9,10,13] require the solutions to the inverse kinematics.…”

Continuum Robots and Magnetic Soft Robots: From Models to Interdisciplinary Challenges for Medical Applications

“…Researchers from different disciplines have proposed various solutions based on their expertise. From a technical perspective, this includes structure [ 39 ] and manufacturing [ 40 ], modeling [ 41 , 42 ], sensing [ 43 , 44 , 45 ], trajectory tracking [ 46 , 47 ], control strategies [ 48 , 49 , 50 ], state estimation [ 51 ], stability analysis [ 52 ], and applications [ 53 , 54 ]. From the viewpoint of the discipline, this encompasses mechanical engineering [ 55 ], computer science [ 56 ], materials [ 57 , 58 , 59 , 60 ], chemistry [ 61 ], biology [ 62 ], and medicine [ 63 ].…”