An active sensing strategy for contact location without tactile sensors using robot geometry and kinematics

Abstract

In this study, we develop new techniques to sense contact locations and control robots in contact situations in order to enable articulated robotic systems to perform manipulations and grasping actions. Active sensing approaches are investigated by utilizing robot kinematics and geometry to improve upon existing sensing methods for contact. Compliant motion control is used so that a robot can actively search for and localize the desired contact location. Robot control in a contact situation is improved by the precise estimation of the contact location. From this viewpoint, we investigate a new control strategy to accommodate the proposed sensing techniques in contact situations. The proposed estimation algorithm and the control strategy both work complementarily. Then, we verify the proposed algorithm through experiments using 7-DOF hardware and a simulation environment. The two major contributions of the proposed active sensing strategy are the estimation algorithm for contact location without any tactile sensors, and the control strategy complementing the proposed estimation algorithm.

Appendix

Lemma 1

Let $\mathfrak {R}^{3}$ denote the set of all ordered 3-tuples of real numbers such as $(x,\, y,\, z)$. We call $\mathfrak {R}^{3}$ a Euclidean space of dimension 3 and ordered 3-tuple points. A geometric object in $\mathfrak {R}^{3}$ is a nonempty subset of $\mathfrak {R}^{3}$. Therefore, a geometric object in $\mathfrak {R}^{3}$ is a nonempty set of points in $\mathfrak {R}^{3}$.

A transformation of $\mathfrak {R}^{3}$ is a 1:1 correspondence between $\mathfrak {R}^{3}$, which is continuous and has a continuous inverse. A transformation that preserves the length is called an isometry.

Let $A$ and $B$ be two geometrical objects in $\mathfrak {R}^{3}$. A continuous map $F_{t} \, :\, \mathfrak {R}^{3} \, \times \, [0,\, 1]\, \rightarrow \, \mathfrak {R}^{3}$ is defined to be an ambient isotopy taking $A$ to $B$. If $F_{0}$ is the identity map $(F_{0} (A)\, =\, A)$, each map $F_{t}$ is an isometry from $\mathfrak {R}^{3}$ to itself, and $F_{1} (A)\, =\, B$. If there is an ambient isotopy taking $A$ to $B$, then $A$ and $B$ are said to be ambient isotopic.

Now if we have a geometric object $A$ and an ambient isotopy $F_{t} \, :\, \mathfrak {R}^{3} \, \times \, [0,\, 1]\, \rightarrow \, \mathfrak {R}^{3}$, then $A$ is continuously transformed to $F_{1} (A)\,$ when the time goes from t = 0 to t = 1. Therefore, $A\cap F_{1} (A)$ is decided by $A$ and $F_{t}$. Therefore, when $A\cap F_{1} (A)$ is not empty, we can determine whether a point in $\mathfrak {R}^{3}$ is contained in $A\cap F_{1}(A)$.