Logic-Skill Programming: An Optimization-based Approach to Sequential Skill Planning

Recent advances in robot skill learning have unlocked the potential to construct task-agnostic skill libraries, facilitating the seamless sequencing of multiple simple manipulation primitives (aka. skills) to tackle significantly more complex tasks. Nevertheless, determining the optimal sequence for independently learned skills remains an open problem, particularly when the objective is given solely in terms of the final geometric configuration rather than a symbolic goal. To address this challenge, we propose Logic-Skill Programming (LSP), an optimization-based approach that sequences independently learned skills to solve long-horizon tasks. We formulate a first-order extension of a mathematical program to optimize the overall cumulative reward of all skills within a plan, abstracted by the sum of value functions. To solve such programs, we leverage the use of Tensor Train to construct the value function space, and rely on alternations between symbolic search and skill value optimization to find the appropriate skill skeleton and optimal subgoal sequence. Experimental results indicate that the obtained value functions provide a superior approximation of cumulative rewards compared to state-of-the-art Reinforcement Learning methods. Furthermore, we validate LSP in three manipulation domains, encompassing both prehensile and non-prehensile primitives. The results demonstrate its capability to identify the optimal solution over the full logic and geometric path. The real-robot experiments showcase the effectiveness of our approach to cope with contact uncertainty and external disturbances in the real world.

Tensor Train for Global Optimization Problems in Robotics

The convergence of many numerical optimization techniques is highly sensitive to the initial guess provided to the solver. We propose an approach based on tensor methods to initialize the existing optimization solvers close to global optima. The approach uses only the definition of the cost function and does not need access to any database of good solutions. We first transform the cost function, which is a function of task parameters and optimization variables, into a probability density function. Unlike existing approaches that set the task parameters as constant, we consider them as another set of random variables and approximate the joint probability distribution of the task parameters and the optimization variables using a surrogate probability model. For a given task, we then generate samples from the conditional distribution with respect to the given task parameter and use them as initialization for the optimization solver. As conditioning and sampling from an arbitrary density function are challenging, we use Tensor Train decomposition to obtain a surrogate probability model from which we can efficiently obtain the conditional model and the samples. The method can produce multiple solutions coming from different modes (when they exist) for a given task. We first evaluate the approach by applying it to various challenging benchmark functions for numerical optimization that are difficult to solve using gradient-based optimization solvers with a naive initialization, showing that the proposed method can produce samples close to the global optima and coming from multiple modes. We then demonstrate the generality of the framework and its relevance to robotics by applying the proposed method to inverse kinematics and motion planning problems with a 7-DoF manipulator.

Ergodic Exploration using Tensor Train: Applications in Insertion Tasks

By generating control policies that create natural search behaviors in autonomous systems, ergodic control provides a principled solution to address tasks that require exploration. A large class of ergodic control algorithms relies on spectral analysis, which suffers 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 paper, we propose a solution for ergodic exploration based on the spectral analysis 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. 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.