[Paper Review] Learning Manifolds for Sequential Motion Planning

Isabel M. Rayas Fernández, Giovanni Sutanto+3 more|arXiv (Cornell University)|Jun 13, 2020

Robotic Path Planning Algorithms23 references4 citations

TL;DR

This paper proposes a data-driven approach to learn implicit constraint manifolds for sequential motion planning using Variational Autoencoders (VAE) and a novel neural network, Equality Constraint Manifold Neural Network (ECoMaNN), which predicts implicit function values. ECoMaNN successfully learns equality constraints from on-manifold demonstration data alone, enabling effective integration into the Sequential Manifold Planning (SMP) framework, with empirical results showing accurate manifold representation and viable motion planning on learned manifolds like spheres and paraboloids.

ABSTRACT

Motion planning with constraints is an important part of many real-world robotic systems. In this work, we study manifold learning methods to learn such constraints from data. We explore two methods for learning implicit constraint manifolds from data: Variational Autoencoders (VAE), and a new method, Equality Constraint Manifold Neural Network (ECoMaNN). With the aim of incorporating learned constraints into a sampling-based motion planning framework, we evaluate the approaches on their ability to learn representations of constraints from various datasets and on the quality of paths produced during planning.

Motivation & Objective

• To address the challenge of learning complex, analytically intractable motion constraints from demonstration data in robotic motion planning.
• To develop a method that learns implicit constraint manifolds without requiring off-manifold data, reducing annotation burden.
• To integrate learned manifolds into the Sequential Manifold Planning (SMP) framework for solving multi-subtask motion planning problems.
• To evaluate the performance of VAEs and ECoMaNN in representing manifold constraints and enabling feasible, low-cost motion plans.

Proposed method

• ECoMaNN is a deep neural network that takes robot configurations as input and outputs the implicit function value h_M(q), learning equality constraints directly from on-manifold demonstrations.
• The network is trained in a supervised manner using only configurations lying on the constraint manifold, avoiding the need for costly off-manifold labeling.
• VAE-based manifold learning is used as a baseline, where the VAE learns a latent space representation and reconstructs configurations to implicitly define the manifold.
• The implicit function value h_M(q) is used to verify whether a configuration lies on the manifold, with values close to zero indicating on-manifold validity.
• The learned manifolds are integrated into the SMP framework, which uses RRT* to find collision-free paths that traverse successive manifolds.
• Evaluation uses both real datasets (e.g., sphere, plane, handover) and synthetic data, with quantitative metrics on h_M(q) mean and standard deviation.

Experimental results

Research questions

• RQ1 Can a neural network learn an implicit representation of equality constraints from on-manifold demonstration data alone, without off-manifold data?
• RQ2 How well can ECoMaNN and VAEs reconstruct the true manifold structure, as measured by implicit function value h_M(q)?
• RQ3 Can learned manifolds from ECoMaNN and VAEs be successfully integrated into the SMP framework to generate feasible, low-cost motion plans?
• RQ4 How do the performance characteristics of ECoMaNN and VAEs compare across different types of constraints (e.g., equality vs. inequality, varying dimensionality)?
• RQ5 To what extent can generated configurations from VAEs remain on the learned manifold, indicating generalization and robustness?

Key findings

• ECoMaNN achieved a mean implicit function value of 0.04 ± 0.06 on the 3D unit sphere dataset, indicating accurate representation of the equality constraint manifold.
• For the Nav dataset (inequality constraint), the VAE produced a mean h_M value of 0.42 ± 0.18, which is below the threshold of 1, confirming adherence to the constraint.
• On generated configurations, the VAE maintained a mean h_M of 0.10 ± 0.03 for the sphere dataset, showing that the model generalizes well to unseen on-manifold points.
• The ECoMaNN model successfully learned the normal space eigenvector field of the sphere manifold, with level set contours close to circular, confirming geometric fidelity.
• A motion planning path was successfully generated on a learned sphere manifold using SMP, demonstrating the feasibility of integrating ECoMaNN into sequential planning frameworks.
• The VAE showed robust performance on the Plane and Orient datasets with mean h_M values of 0.14 ± 0.08 and 0.01 ± 0.01, respectively, indicating effective manifold learning.