Implicit Null-space Manifold Generation for Redundant Robotic Systems

2026-05-25

AI Summary

This work addresses the challenge of globally characterizing the geometric structure of solution manifolds in redundant robotic tasks, which exhibit non-uniqueness and form continuous manifolds in configuration space. Existing approaches struggle to capture these structures comprehensively. The paper proposes a representation-centric implicit modeling paradigm that constructs a scalar field over the configuration space, whose zero-level set precisely coincides with the task-induced solution manifold. By integrating Jacobian-guided neighborhood sampling with implicit neural representations, the method learns a signed distance field of the solution manifold, enabling globally consistent and continuous modeling under arbitrary task mappings—a capability demonstrated for the first time. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator validate the approach’s ability to accurately reconstruct solution manifolds and generalize across varying task parameters.

Abstract

Robotic systems with redundant degrees of freedom can achieve the same task outcome using multiple configurations, resulting in solution sets that form manifolds in the configuration space. Existing approaches typically exploit such redundancy locally through Jacobian-based techniques to compute individual solutions or trajectories. While effective for solution computation, these methods do not retain a representation of the geometry of the solution set itself. In this work, we adopt a representation-centric approach to estimate the geometric structure of the solution space. We consider solution manifolds induced by general task-defining maps and construct an implicit scalar field over the configuration space, whose zero-level set corresponds to the solution manifold. To this end, we generate samples in the neighborhood of the solution manifold using a Jacobian-guided exploration strategy, which efficiently captures its local and global structure. The resulting implicit representation is defined over the configuration space and naturally induces a continuous, distance field that encodes proximity to the solution manifold. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator demonstrate the effectiveness of the proposed representation. Furthermore, the framework enables consistent modeling of solution spaces across families of tasks with continuous variation.

Problem

• redundant robotic systems
• solution manifold
• configuration space
• implicit representation
• task redundancy

Innovation

• Implicit Representation
• Solution Manifold
• Redundant Robotics
• Jacobian-guided Sampling
• Distance Field