Ergodic Exploration using Tensor Train: Applications in Insertion Tasks

By generating control policies that create natural search behaviors, ergodic control provides a principled solution to address tasks that require exploration. Since a large class of ergodic control algorithms relies on spectral analysis, they suffer from the curse-of-dimensionality, both in storage and computation. This drawback has prohibited the application of ergodic control in robot manipulation since it often requires exploration in state space with more than 2 dimensions. Indeed, the original ergodic control formulation will typically not allow exploratory behaviors to be generated for a complete 6D end-effector pose. In this research work, we propose a solution for ergodic exploration in multidimensional spaces using low-rank tensor approximation techniques. We rely on tensor train decomposition, a recent approach from multilinear algebra for low-rank approximation and efficient computation of multidimensional arrays. The proposed solution is efficient both computationally and storage-wise, hence making it suitable for its online implementation in robotic systems.

We leverage our algorithm for high-dimensional ergodic exploration to solve the peg-in-hole insertion problem. We model peg-in-hole insertion task as a target detection problem and use our ergodic controller for the exploration in the 6D state space of the robot end-effector. The approach is applied to a peg-in-hole insertion task using a 7-axis Franka Emika Panda robot, where ergodic exploration allows the task to be achieved without requiring the use of force/torque sensors but only using human demonstrations. The approach can handle uncertainties in the location of the hole and/or graspings of the peg that typically exists in insertion tasks.

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