skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Composable Geometric Motion Policies using Multi-Task Pullback Bundle Dynamical Systems
Despite decades of work in fast reactive planning and control, challenges remain in developing reactive motion policies on non-Euclidean manifolds and enforcing constraints while avoiding undesirable potential function local minima. This work presents a principled method for designing and fusing desired robot task behaviors into a stable robot motion policy, leveraging the geometric structure of non-Euclidean manifolds, which are prevalent in robot configuration and task spaces. Our Pullback Bundle Dynamical Systems (PBDS) framework drives desired task behaviors and prioritizes tasks using separate position-dependent and position/velocity-dependent Riemannian metrics, respectively, thus simplifying individual task design and modular composition of tasks. For enforcing constraints, we provide a class of metric-based tasks, eliminating local minima by imposing non-conflicting potential functions only for goal region attraction. We also provide a geometric optimization problem for combining tasks inspired by Riemannian Motion Policies (RMPs) that reduces to a simple least-squares problem, and we show that our approach is geometrically well-defined. We demonstrate the PBDS framework on the sphere S2 and at 300-500 Hz on a manipulator arm, and we provide task design guidance and an open-source Julia library implementation. Overall, this work presents a fast, easy-to-use framework for generating motion policies without unwanted potential function local minima on general manifolds.  more » « less
Award ID(s):
1931815
PAR ID:
10276529
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
IEEE International Conference on Robotics and Automation
ISSN:
1049-3492
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Simulating soft robots in cluttered environments remains an open problem due to the challenge of capturing complex dynamics and interactions with the environment. Fur- thermore, fast simulation is desired for quickly exploring robot behaviors in the context of motion planning. In this paper, we examine a particular class of inflated-beam soft growing robots called “vine robots,” and present a dynamics simulator that captures general behaviors, handles robot-object interactions, and runs faster than real time. The simulator framework uses a simplified multi-link, rigid-body model with contact constraints. To bridge the sim-to-real gap, we develop methods for fitting model parameters based on video data of a robot in motion and in contact with an environment. We provide examples of simulations, including several with fit parameters, to show the qualitative and quantitative agreement between simulated and real behaviors. Our work demonstrates the capabilities of this high-speed dynamics simulator and its potential for use in the control of soft robots. 
    more » « less
  2. Complex manipulation tasks often require non-trivial and coordinated movements of different parts of a robot. In this work, we address the challenges associated with learning and reproducing the skills required to execute such complex tasks. Specifically, we decompose a task into multiple subtasks and learn to reproduce the subtasks by learning stable policies from demonstrations. By leveraging the RMPflow framework for motion generation, our approach finds a stable global policy in the configuration space that enables simultaneous execution of various learned subtasks. The resulting global policy is a weighted combination of the learned policies such that the motions are coordinated and feasible under the robot's kinematic and environmental constraints. We demonstrate the necessity and efficacy of the proposed approach in the context of multiple constrained manipulation tasks performed by a Franka Emika robot. 
    more » « less
  3. We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an equivariant embedding from the manifold to its image in the Euclidean space. Moreover, intrinsic deep neural networks (iDNNs) incorporate the underlying intrinsic geometry of manifolds via exponential and log maps with respect to a Riemannian structure. Consequently, we prove that the empirical risk of the empirical risk minimizers (ERM) of eDNNs and iDNNs converge in optimal rates. Overall, The eDNNs framework is simple and easy to compute, while the iDNNs framework is accurate and fast converging. To demonstrate the utilities of our framework, various simulation studies, and real data analyses are presented with eDNNs and iDNNs. 
    more » « less
  4. Abstract A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al. (PNAS 113:E7351–E7358, 2016), and later generalized to the Riemannian manifold setting in Duruisseaux and Leok (SJMDS, 2022a). This variational framework was exploited on normed vector spaces in Duruisseaux et al. (SJSC 43:A2949–A2980, 2021) using time-adaptive geometric integrators to design efficient explicit algorithms for symplectic accelerated optimization, and it was observed that geometric discretizations which respect the time-rescaling invariance and symplecticity of the Lagrangian and Hamiltonian flows were substantially less prone to stability issues, and were therefore more robust, reliable, and computationally efficient. As such, it is natural to develop time-adaptive Hamiltonian variational integrators for accelerated optimization on Riemannian manifolds. In this paper, we consider the case of Riemannian manifolds embedded in a Euclidean space that can be characterized as the level set of a submersion. We will explore how holonomic constraints can be incorporated in discrete variational integrators to constrain the numerical discretization of the Riemannian Hamiltonian system to the Riemannian manifold, and we will test the performance of the resulting algorithms by solving eigenvalue and Procrustes problems formulated as optimization problems on the unit sphere and Stiefel manifold. 
    more » « less
  5. The field of end-user robot programming seeks to develop methods that empower non-expert programmers to task and modify robot operations. In doing so, researchers may enhance robot flexibility and broaden the scope of robot deployments into the real world. We introduce PRogramAR (Programming Robots using Augmented Reality), a novel end-user robot programming system that combines the intuitive visual feedback of augmented reality (AR) with the simplistic and responsive paradigm of trigger-action programming (TAP) to facilitate human-robot collaboration. Through PRogramAR, users are able to rapidly author task rules and desired reactive robot behaviors, while specifying task constraints and observing program feedback contextualized directly in the real world. PRogramAR provides feedback by simulating the robot’s intended behavior and providing instant evaluation of TAP rule executability to help end users better understand and debug their programs during development. In a system validation, 17 end users ranging from ages 18 to 83 used PRogramAR to program a robot to assist them in completing three collaborative tasks. Our results demonstrate how merging the benefits of AR and TAP using elements from prior robot programming research into a single novel system can successfully enhance the robot programming process for non-expert users. 
    more » « less