A Workspace Limit Approach for Teleoperation Based on Signed Distance Function

Abstract

The workspace limit to smoothly map unreachable motions sensed in the leader side$^1$ to the reachable workspace of the follower robot is fundamental for teleoperation systems. Although numerous workspace determination methods have been studied, the workspace limit approach still remains challenging. The main difficulty is that the computation of the mapping from an unreachable point to its corresponding nearest point on the workspace boundary is time-consuming. Here we propose a novel representation method to describe the geometric information of the workspace by using Signed Distance Function (SDF). Compared with existing SDFs, the corresponding nearest points on the boundary for unreachable points are also pre-computed and stored. Based on this representation method, we present a time-saving workspace limit approach. The discontinuity problem inherited from the discretized SDF is addressed by an interpolation method. Since the geometric information of the workspace is represented and pre-computed by the SDF, the time-consuming searching is replaced by a simple and extremely fast lookup from the stored SDF values with time complexity O(1). The proposed approach has been implemented for a Single-Leader/Single-Follower (SLSF) teleoperation system. The experimental results demonstrate the effectiveness and advantages of the proposed approach.