Expansion-GRR: Efficient Generation of Smooth Global Redundancy Resolution Roadmaps

TL;DR

This work introduces a novel method EXPANSION-GRR that leverages efficient configuration space projections and enables a rapid generation of smooth roadmaps that satisfy the task constraints and proposes a simple multi-seed strategy that further enhances the final quality.

Abstract

Global redundancy resolution (GRR) roadmaps is a novel concept in robotics that facilitates the mapping from task space paths to configuration space paths in a legible, predictable, and repeatable way. Such roadmaps could find widespread utility in applications such as safe teleoperation, consistent path planning, and motion primitives generation. However, previous methods to compute GRR roadmaps often necessitate a lengthy computation time and produce non-smooth paths, limiting their practical efficacy. To address this challenge, we introduce a novel method Expansion-GRR that leverages efficient configuration space projections and enables rapid generation of smooth roadmaps that satisfy the task constraints. Additionally, we propose a simple multi-seed strategy that further enhances the final quality. We conducted experiments in simulation with a 5-link planar manipulator and a Kinova arm. We were able to generate the Expansion-GRR roadmaps up to 2 orders of magnitude faster while achieving higher smoothness. We also demonstrate the utility of the GRR roadmaps in teleoperation tasks where our method outperformed prior methods and reactive IK solvers in terms of success rate and solution quality.

Figures (6)

• Figure 1: The Kinova arm is tasked with reaching a 6-dof pose to pick up an object. For this task, the 7-dof arm is kinematically redundant and can reach the same object position with multiple configurations.
• Figure 2: (a) After a cyclic path, non-global resolution can lead to different ending configurations from the same starting point. (b) Global resolution results in consistent paths, where the robot always returns to the original configuration.
• Figure 3: An illustration of the roadmaps $G_p$ and $G_q$. (a) The points $p_1, p_2$, and $p_3$ are neighboring samples in $\mathcal{T}$-space, in this case, the end-effector position in $\mathbb{R}^{2}$. (b) The solid lines indicate smm of $\mathcal{T}$-space points. A roadmap $G_q$ must select a single configuration $q_i$ from each manifold, and additionally, ensure that the configurations, $q_1, q_2$ and $q_3$ of adjacent points, are "close enough" to pertain continuity and smooth transition in $\mathcal{C}$-space.
• Figure 4: An illustration of the continuity constraint. (a) The robot's end-effector follows a straight path $P_p$ from $p_i$ to its adjacent point $p_j$ in $\mathcal{T}$-space (green). (b) The robot's corresponding configuration path $P_q$ from $q_i$ to $q_j$ in $\mathcal{C}$-space (green) can be computed by projecting the intermediate configurations to their corresponding smm in a bisection manner. Ideally, $P_q$ should stay "close" to the straight line $L_q$ delineated by $q_i$ and $q_j$ (black).
• Figure 5: An illustration of projecting from multiple neighbors. (a) The points $p_1, p_2$, and $p_3$ are neighboring points of $p$ in $\mathcal{T}$-space. (b) The solid lines indicate the self-motion manifold of $p$. A weighted average $q_{avg}$ is computed with neighbors' corresponding configurations $q_1$, $q_2$, and $q_3$ in $\mathcal{C}$-space. It is then projected onto the self-motion manifold to find $q$.