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Logic-Skill Programming: An Optimization-based Approach to Sequential Skill Planning
May 07, 2024
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.
A Minimum-Jerk Approach to Handle Singularities in Virtual Fixtures
May 06, 2024Implementing virtual fixtures in guiding tasks constrains the movement of the robot's end effector to specific curves within its workspace. However, incorporating guiding frameworks may encounter discontinuities when optimizing the reference target position to the nearest point relative to the current robot position. This article aims to give a geometric interpretation of such discontinuities, with specific reference to the commonly adopted Gauss-Newton algorithm. The effect of such discontinuities, defined as Euclidean Distance Singularities, is experimentally proved. We then propose a solution that is based on a Linear Quadratic Tracking problem with minimum jerk command, then compare and validate the performances of the proposed framework in two different human-robot interaction scenarios.
Logic Dynamic Movement Primitives for Long-horizon Manipulation Tasks in Dynamic Environments
Apr 24, 2024Learning from Demonstration (LfD) stands as an efficient framework for imparting human-like skills to robots. Nevertheless, designing an LfD framework capable of seamlessly imitating, generalizing, and reacting to disturbances for long-horizon manipulation tasks in dynamic environments remains a challenge. To tackle this challenge, we present Logic Dynamic Movement Primitives (Logic-DMP), which combines Task and Motion Planning (TAMP) with an optimal control formulation of DMP, allowing us to incorporate motion-level via-point specifications and to handle task-level variations or disturbances in dynamic environments. We conduct a comparative analysis of our proposed approach against several baselines, evaluating its generalization ability and reactivity across three long-horizon manipulation tasks. Our experiment demonstrates the fast generalization and reactivity of Logic-DMP for handling task-level variants and disturbances in long-horizon manipulation tasks.
Planning for Robust Open-loop Pushing: Exploiting Quasi-static Belief Dynamics and Contact-informed Optimization
Apr 03, 2024Non-prehensile manipulation such as pushing is typically subject to uncertain, non-smooth dynamics. However, modeling the uncertainty of the dynamics typically results in intractable belief dynamics, making data-efficient planning under uncertainty difficult. This article focuses on the problem of efficiently generating robust open-loop pushing plans. First, we investigate how the belief over object configurations propagates through quasi-static contact dynamics. We exploit the simplified dynamics to predict the variance of the object configuration without sampling from a perturbation distribution. In a sampling-based trajectory optimization algorithm, the gain of the variance is constrained in order to enforce robustness of the plan. Second, we propose an informed trajectory sampling mechanism for drawing robot trajectories that are likely to make contact with the object. This sampling mechanism is shown to significantly improve chances of finding robust solutions, especially when making-and-breaking contacts is required. We demonstrate that the proposed approach is able to synthesize bi-manual pushing trajectories, resulting in successful long-horizon pushing maneuvers without exteroceptive feedback such as vision or tactile feedback.
An Optimal Control Formulation of Tool Affordance Applied to Impact Tasks
Feb 09, 2024Humans use tools to complete impact-aware tasks such as hammering a nail or playing tennis. The postures adopted to use these tools can significantly influence the performance of these tasks, where the force or velocity of the hand holding a tool plays a crucial role. The underlying motion planning challenge consists of grabbing the tool in preparation for the use of this tool with an optimal body posture. Directional manipulability describes the dexterity of force and velocity in a joint configuration along a specific direction. In order to take directional manipulability and tool affordances into account, we apply an optimal control method combining iterative linear quadratic regulator(iLQR) with the alternating direction method of multipliers(ADMM). Our approach considers the notion of tool affordances to solve motion planning problems, by introducing a cost based on directional velocity manipulability. The proposed approach is applied to impact tasks in simulation and on a real 7-axis robot, specifically in a nail-hammering task with the assistance of a pilot hole. Our comparison study demonstrates the importance of maximizing directional manipulability in impact-aware tasks.
Tactile Ergodic Control Using Diffusion and Geometric Algebra
Feb 07, 2024Continuous physical interaction between robots and their environment is a requirement in many industrial and household tasks, such as sanding and cleaning. Due to the complex tactile information, these tasks are notoriously difficult to model and to sense. In this article, we introduce a closed-loop control method that is constrained to surfaces. The applications that we target have in common that they can be represented by probability distributions on the surface that correlate to the time the robot should spend in a region. These surfaces can easily be captured jointly with the target distributions using coloured point clouds. We present the extension of an ergodic control approach that can be used with point clouds, based on heat equation-driven area coverage (HEDAC). Our method enables closed-loop exploration by measuring the actual coverage using vision. Unlike existing approaches, we approximate the potential field from non-stationary diffusion using spectral acceleration, which does not require complex preprocessing steps and achieves real-time closed-loop control frequencies. We exploit geometric algebra to stay in contact with the target surface by tracking a line while simultaneously exerting a desired force along that line. Our approach is suitable for fully autonomous and human-robot interaction settings where the robot can either directly measure the coverage of the target with its sensors or by being guided online by markings or annotations of a human expert. We tested the performance of the approach in kinematic simulation using point clouds, ranging from the Stanford bunny to a variety of kitchen utensils. Our real-world experiments demonstrate that the proposed approach can successfully be used to wash kitchenware with curved surfaces, by cleaning the dirt detected by vision in an online manner. Website: https://geometric-algebra.tobiloew.ch/tactile_ergodic_control
AiRLIHockey: Highly Reactive Contact Control and Stochastic Optimal Shooting
Jan 26, 2024Air hockey is a highly reactive game which requires the player to quickly reason over stochastic puck and contact dynamics. We implement a hierarchical framework which combines stochastic optimal control for planning shooting angles and sampling-based model-predictive control for continuously generating constrained mallet trajectories. Our agent was deployed and evaluated in simulation and on a physical setup as part of the Robot Air-Hockey challenge competition at NeurIPS 2023.
Online Learning of Piecewise Polynomial Signed Distance Fields for Manipulation Tasks
Jan 15, 2024Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online method for learning implicit representations of signed distance using piecewise polynomial basis functions. Starting from an arbitrary prior shape, our approach incrementally constructs a continuous representation from incoming point cloud data. It offers fast access to distance and analytical gradients without the need to store training data. We assess the accuracy of our model on a diverse set of household objects and compare it to neural network and Gaussian process counterparts. Distance reconstruction and real-time updates are further evaluated in a physical experiment by simultaneously collecting sparse point cloud data and using the evolving model to control a manipulator.
D-LGP: Dynamic Logic-Geometric Program for Combined Task and Motion Planning
Dec 05, 2023Many real-world sequential manipulation tasks involve a combination of discrete symbolic search and continuous motion planning, collectively known as combined task and motion planning (TAMP). However, prevailing methods often struggle with the computational burden and intricate combinatorial challenges stemming from the multitude of action skeletons. To address this, we propose Dynamic Logic-Geometric Program (D-LGP), a novel approach integrating Dynamic Tree Search and global optimization for efficient hybrid planning. Through empirical evaluation on three benchmarks, we demonstrate the efficacy of our approach, showcasing superior performance in comparison to state-of-the-art techniques. We validate our approach through simulation and demonstrate its capability for online replanning under uncertainty and external disturbances in the real world.
Extending the Cooperative Dual-Task Space in Conformal Geometric Algebra
Oct 29, 2023
In this work, we are presenting an extension of the cooperative dual-task space (CDTS) in conformal geometric algebra. The CDTS was first defined using dual quaternion algebra and is a well established framework for the simplified definition of tasks using two manipulators. By integrating conformal geometric algebra, we aim to further enhance the geometric expressiveness and thus simplify the modeling of various tasks. We show this formulation by first presenting the CDTS and then its extension that is based around a cooperative pointpair. This extension keeps all the benefits of the original formulation that is based on dual quaternions, but adds more tools for geometric modeling of the dual-arm tasks. We also present how this CGA-CDTS can be seamlessly integrated with an optimal control framework in geometric algebra that was derived in previous work. In the experiments, we demonstrate how to model different objectives and constraints using the CGA-CDTS. Using a setup of two Franka Emika robots we then show the effectiveness of our approach using model predictive control in real world experiments.