A Survey on Path Planning Problem of Rolling Contacts: Approaches, Applications and Future Challenges

TL;DR

The paper surveys path planning for rolling contacts, spanning single-contact spin-rolling to multi-contact and swarm-like scenarios. It integrates Montana kinematics with generalized curvature-based models and analyzes both S-CR and M-CR planning approaches, including incremental, mirrored, and sub-system strategies. The review covers robotic applications from ballbots and spherical robots to dexterous manipulation, nonprehensile tasks, reconfigurable swarms, and micro/nano particle manipulation, while highlighting core challenges such as nonholonomic constraints, slip-induced drift, and topological complexity (e.g., $\mathbf{v} = \mathbf{v}' + \boldsymbol{\omega} \times \mathbf{r}$). It clarifies how geometric mechanics informs planning algorithms and outlines future directions for integrating dynamics, sensing, and control to enable robust rolling-contact robotics.

Abstract

This paper explores an eclectic range of path-planning methodologies engineered for rolling surfaces. Our focus is on the kinematic intricacies of rolling contact systems, which are investigated through a motion planning lens. Beyond summarizing the approaches to single-contact rotational surfaces, we explore the challenging domain of spin-rolling multi-contact systems. Our work proposes solutions for the higher-dimensional problem of multiple rotating objects in contact. Venturing beyond kinematics, these methodologies find application across a spectrum of domains, including rolling robots, reconfigurable swarm robotics, micro/nano manipulation, and nonprehensile manipulations. Through meticulously examining established planning strategies, we unveil their practical implementations in various real-world scenarios, from intricate dexterous manipulation tasks to the nimble manoeuvring of rolling robots and even shape planning of multi-contact swarms of particles. This study introduces the persistent challenges and unexplored frontiers of robotics, intricately linked to both path planning and mechanism design. As we illuminate existing solutions, we also set the stage for future breakthroughs in this dynamic and rapidly evolving field by highlighting the critical importance of addressing rolling contact problems.

Figures (8)

• Figure 1: Different characteristics in rolling contact problem. Applications: a) ball-bot robot fankhauser2010modeling, b) rolling spherical robots armour2006rolling, c) agile grasping yuan2020designIROS, d) foot placement in legged robots hutter2014quadrupedal, e) power grasping teeple2020multi, f) reconfigurable rolling robots zhong2022kin, g) mico-/nano-particle manipulation sumer2008rolling, h) nonprehensile manipulation woordrufLynch2023TRO, i) wheels in mobile robot/cars tafrishi2022novel, j) Soft hand grasping and manipulation gilday2023predictive.
• Figure 2: The path planning of $i$ number of spin-rolling convex off-rotating surfaces/fingers $U_{f,i}$ on an arbitrary surface of the main trapped object $U_o$.
• Figure 3: Simulation results of some well-known motion planning strategies for the rolling contact kinematics.
• Figure 4: An incremental path planning problem strategy for M-CR.
• Figure 5: An example scenario for six rotating objects with arbitrary main surface objects. Note that for simplicity the rotating objects are assumed simple disks with random radii.