# Ergodic Exploration using Tensor Train: Applications in Insertion Tasks

arXiv: https://arxiv.org/abs/2101.04428 · HTML: https://mlsanity.com/paper/2101.04428/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2021.

## Built on by (most cited first, 7 of 7)

- [CACTO: Continuous Actor-Critic with Trajectory Optimization -- Towards global optimality](https://mlsanity.com/paper/2211.06625/) (2022)
- [Fast Ergodic Search with Kernel Functions](https://mlsanity.com/paper/2403.01536/) (2024)
- [BiRP: Learning Robot Generalized Bimanual Coordination using Relative Parameterization Method on Human Demonstration](https://mlsanity.com/paper/2307.05933/) (2023)
- [Flow Matching Ergodic Coverage](https://mlsanity.com/paper/2504.17872/) (2025)
- [Tensor Train for Global Optimization Problems in Robotics](https://mlsanity.com/paper/2206.05077/) (2022)
- [Volumetric Ergodic Control](https://mlsanity.com/paper/2511.11533/) (2025)
- [TRACE: Ergodic Trajectory Optimization for Active Scene Reconstruction](https://mlsanity.com/paper/2608.02304/) (2026)

## Abstract (arXiv)

In robotics, ergodic control extends the tracking principle by specifying a probability distribution over an area to cover instead of a trajectory to track. The original problem is formulated as a spectral multiscale coverage problem, typically requiring the spatial distribution to be decomposed as Fourier series. This approach does not scale well to control problems requiring exploration in search space of more than 2 dimensions. To address this issue, we propose the use of tensor trains, a recent low-rank tensor decomposition technique from the field of multilinear algebra. The proposed solution is efficient, both computationally and storage-wise, hence making it suitable for its online implementation in robotic systems. The approach is applied to a peg-in-hole insertion task requiring full 6D end-effector poses, implemented with a 7-axis Franka Emika Panda robot. In this experiment, ergodic exploration allows the task to be achieved without requiring the use of force/torque sensors.