SE(3) Linear Parameter Varying Dynamical Systems for Globally Asymptotically Stable End-Effector Control

Linear Parameter Varying Dynamical Systems (LPV-DS) encode trajectories into an autonomous first-order DS that enables reactive responses to perturbations, while ensuring globally asymptotic stability at the target. However, the current LPV-DS framework is established on Euclidean data only and has not been applicable to broader robotic applications requiring pose control. In this paper we present an extension to the current LPV-DS framework, named Quaternion-DS, which efficiently learns a DS-based motion policy for orientation. Leveraging techniques from differential geometry and Riemannian statistics, our approach properly handles the non-Euclidean orientation data in quaternion space, enabling the integration with positional control, namely SE(3) LPV-DS, so that the synergistic behaviour within the full SE(3) pose is preserved. Through simulation and real robot experiments, we validate our method, demonstrating its ability to efficiently and accurately reproduce the original SE(3) trajectory while exhibiting strong robustness to perturbations in task space.

Constrained Passive Interaction Control: Leveraging Passivity and Safety for Robot Manipulators

Passivity is necessary for robots to fluidly collaborate and interact with humans physically. Nevertheless, due to the unconstrained nature of passivity-based impedance control laws, the robot is vulnerable to infeasible and unsafe configurations upon physical perturbations. In this paper, we propose a novel control architecture that allows a torque-controlled robot to guarantee safety constraints such as kinematic limits, self-collisions, external collisions and singularities and is passive only when feasible. This is achieved by constraining a dynamical system based impedance control law with a relaxed hierarchical control barrier function quadratic program subject to multiple concurrent, possibly contradicting, constraints. Joint space constraints are formulated from efficient data-driven self- and external C^2 collision boundary functions. We theoretically prove constraint satisfaction and show that the robot is passive when feasible. Our approach is validated in simulation and real robot experiments on a 7DoF Franka Research 3 manipulator.

Object Permanence Filter for Robust Tracking with Interactive Robots

Object permanence, which refers to the concept that objects continue to exist even when they are no longer perceivable through the senses, is a crucial aspect of human cognitive development. In this work, we seek to incorporate this understanding into interactive robots by proposing a set of assumptions and rules to represent object permanence in multi-object, multi-agent interactive scenarios. We integrate these rules into the particle filter, resulting in the Object Permanence Filter (OPF). For multi-object scenarios, we propose an ensemble of K interconnected OPFs, where each filter predicts plausible object tracks that are resilient to missing, noisy, and kinematically or dynamically infeasible measurements, thus bringing perceptional robustness. Through several interactive scenarios, we demonstrate that the proposed OPF approach provides robust tracking in human-robot interactive tasks agnostic to measurement type, even in the presence of prolonged and complete occlusion. Webpage: https://opfilter.github.io/.

On the Feasibility of EEG-based Motor Intention Detection for Real-Time Robot Assistive Control

This paper explores the feasibility of employing EEG-based intention detection for real-time robot assistive control. We focus on predicting and distinguishing motor intentions of left/right arm movements by presenting: i) an offline data collection and training pipeline, used to train a classifier for left/right motion intention prediction, and ii) an online real-time prediction pipeline leveraging the trained classifier and integrated with an assistive robot. Central to our approach is a rich feature representation composed of the tangent space projection of time-windowed sample covariance matrices from EEG filtered signals and derivatives; allowing for a simple SVM classifier to achieve unprecedented accuracy and real-time performance. In pre-recorded real-time settings (160 Hz), a peak accuracy of 86.88% is achieved, surpassing prior works. In robot-in-the-loop settings, our system successfully detects intended motion solely from EEG data with 70% accuracy, triggering a robot to execute an assistive task. We provide a comprehensive evaluation of the proposed classifier.

Neural Contractive Dynamical Systems

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural networks. We propose a novel methodology to learn neural contractive dynamical systems, where our neural architecture ensures contraction, and hence, global stability. To efficiently scale the method to high-dimensional dynamical systems, we develop a variant of the variational autoencoder that learns dynamics in a low-dimensional latent representation space while retaining contractive stability after decoding. We further extend our approach to learning contractive systems on the Lie group of rotations to account for full-pose end-effector dynamic motions. The result is the first highly flexible learning architecture that provides contractive stability guarantees with capability to perform obstacle avoidance. Empirically, we demonstrate that our approach encodes the desired dynamics more accurately than the current state-of-the-art, which provides less strong stability guarantees.

Learning Realistic Joint Space Boundaries for Range of Motion Analysis of Healthy and Impaired Human Arms

A realistic human kinematic model that satisfies anatomical constraints is essential for human-robot interaction, biomechanics and robot-assisted rehabilitation. Modeling realistic joint constraints, however, is challenging as human arm motion is constrained by joint limits, inter- and intra-joint dependencies, self-collisions, individual capabilities and muscular or neurological constraints which are difficult to represent. Hence, physicians and researchers have relied on simple box-constraints, ignoring important anatomical factors. In this paper, we propose a data-driven method to learn realistic anatomically constrained upper-limb range of motion (RoM) boundaries from motion capture data. This is achieved by fitting a one-class support vector machine to a dataset of upper-limb joint space exploration motions with an efficient hyper-parameter tuning scheme. Our approach outperforms similar works focused on valid RoM learning. Further, we propose an impairment index (II) metric that offers a quantitative assessment of capability/impairment when comparing healthy and impaired arms. We validate the metric on healthy subjects physically constrained to emulate hemiplegia and different disability levels as stroke patients.

Towards Feasible Dynamic Grasping: Leveraging Gaussian Process Distance Field, SE(3) Equivariance and Riemannian Mixture Models

In this paper, we present a novel approach towards feasible dynamic grasping by leveraging Gaussian Process Distance Fields (GPDF), SE(3) equivariance, and Riemannian Mixture Models. We seek to improve the grasping capabilities of robots in dynamic tasks where objects may be moving. The proposed method combines object shape reconstruction, grasp sampling, and grasp pose selection to enable effective grasping in such scenarios. By utilizing GPDF, the approach accurately models the shape and physical properties of objects, allowing for precise grasp planning. SE(3) equivariance ensures that the sampled grasp poses are equivariant to the object's pose. Additionally, Riemannian Gaussian Mixture Models are employed to test reachability, providing a feasible and adaptable grasping strategy. The sampled feasible grasp poses are used as targets for novel task or joint space reactive controllers formulated by Gaussian Mixture Models and Gaussian Processes, respectively. Experimental results demonstrate the effectiveness of the proposed approach in generating feasible grasp poses and successful grasping in dynamic environments. (Video: https://www.youtube.com/watch?v=wjIVrwTzTOc&t=70s)

DAMM: Directionality-Aware Mixture Model Parallel Sampling for Efficient Dynamical System Learning

The Linear Parameter Varying Dynamical System (LPV-DS) is a promising framework for learning stable time-invariant motion policies in robot control. By employing statistical modeling and semi-definite optimization, LPV-DS encodes complex motions via non-linear DS, ensuring the robustness and stability of the system. However, the current LPV-DS scheme faces challenges in accurately interpreting trajectory data while maintaining model efficiency and computational efficiency. To address these limitations, we propose the Directionality-aware Mixture Model (DAMM), a new statistical model that leverages Riemannian metric on $d$-dimensional sphere $\mathbb{S}^d$, and efficiently incorporates non-Euclidean directional information with position. Additionally, we introduce a hybrid Markov chain Monte Carlo method that combines the Gibbs Sampling and the Split/Merge Proposal, facilitating parallel computation and enabling faster inference for near real-time learning performance. Through extensive empirical validation, we demonstrate that the improved LPV-DS framework with DAMM is capable of producing physically-meaningful representations of the trajectory data and improved performance of the generated DS while showcasing significantly enhanced learning speed compared to its previous iterations.

Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies

Dynamical System (DS) based Learning from Demonstration (LfD) allows learning of reactive motion policies with stability and convergence guarantees from a few trajectories. Yet, current DS learning techniques lack the flexibility to generalize to new task instances as they ignore explicit task parameters that inherently change the underlying trajectories. In this work, we propose Elastic-DS, a novel DS learning, and generalization approach that embeds task parameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying (LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMM constrained to SE(3) task-relevant frames. Given a new task instance/context, the Elastic-GMM is transformed with Laplacian Editing and used to re-estimate the LPV-DS policy. Elastic-DS is compositional in nature and can be used to construct flexible multi-step tasks. We showcase its strength on a myriad of simulated and real-robot experiments while preserving desirable control-theoretic guarantees. Supplementary videos can be found at https://sites.google.com/view/elastic-ds