Mesh Manifold based Riemannian Motion Planning for Omnidirectional Micro Aerial Vehicles (2102.10313v1)

Abstract: This paper presents a novel on-line path planning method that enables aerial robots to interact with surfaces. We present a solution to the problem of finding trajectories that drive a robot towards a surface and move along it. Triangular meshes are used as a surface map representation that is free of fixed discretization and allows for very large workspaces. We propose to leverage planar parametrization methods to obtain a lower-dimensional topologically equivalent representation of the original surface. Furthermore, we interpret the original surface and its lower-dimensional representation as manifold approximations that allow the use of Riemannian Motion Policies (RMPs), resulting in an efficient, versatile, and elegant motion generation framework. We compare against several Rapidly-exploring Random Tree (RRT) planners, a customized CHOMP variant, and the discrete geodesic algorithm. Using extensive simulations on real-world data we show that the proposed planner can reliably plan high-quality near-optimal trajectories at minimal computational cost. The accompanying multimedia attachment demonstrates feasibility on a real OMAV. The obtained paths show less than 10% deviation from the theoretical optimum while facilitating reactive re-planning at kHz refresh rates, enabling flying robots to perform motion planning for interaction with complex surfaces.

• The paper introduces a novel mesh manifold approach leveraging Riemannian motion policies for efficient surface navigation of OMAVs.
• It presents a 2D-3D parametrization method that maps surfaces while preserving topology for smooth, computationally light trajectory generation.
• Experimental results demonstrate high planning success with kHz refresh rates and trajectories deviating less than 10% from optimal.

Overview of "Mesh Manifold based Riemannian Motion Planning for Omnidirectional Micro Aerial Vehicles"

This paper introduces a novel motion planning framework aimed at enabling omnidirectional micro aerial vehicles (OMAVs) to effectively navigate and interact with complex surfaces. The core innovation lies in leveraging surface mesh representations and employing Riemannian Motion Policies (RMPs) to achieve efficient and accurate path planning for aerial robots engaged in tasks like inspection and surface interaction.

Contributions and Methodology

The researchers present a method to address two significant challenges in aerial robot planning: scaling of map representations and planning trajectories relative to surfaces. Traditional discretized map representations, like voxel grids, are limited by fixed resolution and size constraints, which are ill-suited for vast workspaces encountered by OMAVs. This paper proposes using triangular meshes as a surface representation that bypasses these constraints. By interpreting these meshes as approximations of smooth Riemannian manifolds, the authors derive a mathematically grounded strategy for surface navigation.

The approach encompasses several key contributions:

• 2D-3D Parametrization: The authors develop an efficient parametrization technique that maps a 3D mesh surface onto a 2D representation while retaining topological equivalence. This mapping allows the planning algorithm to exploit the geometric connectedness of the surface.
• Riemannian Motion Policies: The paper utilizes RMPs to combine multiple motion policies formulated on the lower-dimensional mesh manifold. By implementing policies that guide the OMAV towards and along a surface, the framework ensures smooth trajectory generation with minimal computational overhead.
• Policy Combination and Implementation: They detail the formulation of separate policies for surface attraction and following, which are optimally combined to produce trajectories that approach the theoretical optimum with less than 10% deviation.

Evaluation and Results

The proposed planning method is rigorously tested against several existing methods, including different RRT algorithms and CHOMP. Using real-world data, it demonstrates superior performance in terms of planning success rates, computational efficiency, and trajectory quality. Notably, the planner achieves kHz refresh rates, enabling reactive replanning capabilities crucial for dynamic interaction tasks.

The RMP-based planner consistently outperforms the alternative methods in terms of computational time, maintaining an execution duration on the order of microseconds per iteration. Trajectories generated are notably smooth, largely due to the continuous acceleration fields in the Riemannian framework rather than discrete point-to-point planning seen in sampling-based approaches.

Implications and Future Directions

This work provides a solid foundation for improving the efficacy of OMAVs in surface-related tasks. The seamless integration of real-time data and high refresh rates offers potential for reactive planning—a necessary condition for applications in uncertain environments. Practically, this could enhance operations in industrial inspection, maintenance tasks, and emergency response, where precise interaction with surfaces is essential.

From a theoretical perspective, the paper expands the application of manifold-based approaches to motion planning, showcasing the adaptability of RMPs in diverse robotic contexts. Future research could explore combining these methods with machine learning models to optimize interaction strategies based on learned surface properties or integrating sensory feedback for enhanced interaction in unknown environments.

In sum, the paper presents a robust framework that combines the mathematical rigor of Riemannian geometry with practical considerations of aerial robotics, paving the way for more sophisticated and reliable aerial interaction systems.