Learning Dynamical Systems Encoding Non-Linearity within Space Curvature

Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of real-world scenarios necessitates DS with a higher degree of non-linearity, along with the ability to adapt to potential changes in environmental conditions, such as obstacles. Current learning strategies for DSs often involve a trade-off, sacrificing either stability guarantees or offline computational efficiency in order to enhance the capabilities of the learned DS. Online local adaptation to environmental changes is either not taken into consideration or treated as a separate problem. In this paper, our objective is to introduce a method that enhances the complexity of the learned DS without compromising efficiency during training or stability guarantees. Furthermore, we aim to provide a unified approach for seamlessly integrating the initially learned DS's non-linearity with any local non-linearities that may arise due to changes in the environment. We propose a geometrical approach to learn asymptotically stable non-linear DS for robotics control. Each DS is modeled as a harmonic damped oscillator on a latent manifold. By learning the manifold's Euclidean embedded representation, our approach encodes the non-linearity of the DS within the curvature of the space. Having an explicit embedded representation of the manifold allows us to showcase obstacle avoidance by directly inducing local deformations of the space. We demonstrate the effectiveness of our methodology through two scenarios: first, the 2D learning of synthetic vector fields, and second, the learning of 3D robotic end-effector motions in real-world settings.

Learning Barrier-Certified Polynomial Dynamical Systems for Obstacle Avoidance with Robots

Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose incorporating barrier certificates into an optimization problem to learn a stable and barrier-certified DS. Such optimization problem can be very complex or extremely conservative when the traditional linear parameter-varying formulation is used. Thus, different from previous approaches in the literature, we propose to use polynomial representations for DSs, which yields an optimization problem that can be tackled by sum-of-squares techniques. Finally, our approach can handle obstacle shapes that fall outside the scope of assumptions typically found in the literature concerning obstacle avoidance within the DS learning framework. Supplementary material can be found at the project webpage: https://martinschonger.github.io/abc-ds

Transfer Learning in Robotics: An Upcoming Breakthrough? A Review of Promises and Challenges

Transfer learning is a conceptually-enticing paradigm in pursuit of truly intelligent embodied agents. The core concept -- reusing prior knowledge to learn in and from novel situations -- is successfully leveraged by humans to handle novel situations. In recent years, transfer learning has received renewed interest from the community from different perspectives, including imitation learning, domain adaptation, and transfer of experience from simulation to the real world, among others. In this paper, we unify the concept of transfer learning in robotics and provide the first taxonomy of its kind considering the key concepts of robot, task, and environment. Through a review of the promises and challenges in the field, we identify the need of transferring at different abstraction levels, the need of quantifying the transfer gap and the quality of transfer, as well as the dangers of negative transfer. Via this position paper, we hope to channel the effort of the community towards the most significant roadblocks to realize the full potential of transfer learning in robotics.

Implicit Manifold Gaussian Process Regression

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this technique to higher dimensions is to leverage the implicit low-dimensional manifold upon which the data actually lies, as postulated by the manifold hypothesis. Prior work ordinarily requires the manifold structure to be explicitly provided though, i.e. given by a mesh or be known to be one of the well-known manifolds like the sphere. In contrast, in this paper we propose a Gaussian process regression technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way. For the resulting model, we discuss its convergence to the Mat\'ern Gaussian process on the assumed manifold. Our technique scales up to hundreds of thousands of data points, and may improve the predictive performance and calibration of the standard Gaussian process regression in high-dimensional~settings.

Differentiable Robot Neural Distance Function for Adaptive Grasp Synthesis on a Unified Robotic Arm-Hand System

Grasping is a fundamental skill for robots to interact with their environment. While grasp execution requires coordinated movement of the hand and arm to achieve a collision-free and secure grip, many grasp synthesis studies address arm and hand motion planning independently, leading to potentially unreachable grasps in practical settings. The challenge of determining integrated arm-hand configurations arises from its computational complexity and high-dimensional nature. We address this challenge by presenting a novel differentiable robot neural distance function. Our approach excels in capturing intricate geometry across various joint configurations while preserving differentiability. This innovative representation proves instrumental in efficiently addressing downstream tasks with stringent contact constraints. Leveraging this, we introduce an adaptive grasp synthesis framework that exploits the full potential of the unified arm-hand system for diverse grasping tasks. Our neural joint space distance function achieves an 84.7% error reduction compared to baseline methods. We validated our approaches on a unified robotic arm-hand system that consists of a 7-DoF robot arm and a 16-DoF multi-fingered robotic hand. Results demonstrate that our approach empowers this high-DoF system to generate and execute various arm-hand grasp configurations that adapt to the size of the target objects while ensuring whole-body movements to be collision-free.

A Structured Prediction Approach for Robot Imitation Learning

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised learning that enables learning models to operate on output spaces with complex structures. Through the lens of structured prediction, we show how robots can learn to imitate trajectories belonging to not only Euclidean spaces but also Riemannian manifolds. Exploiting ideas from information theory, we propose a class of loss functions based on the f-divergence to measure the information loss between the demonstrated and reproduced probabilistic trajectories. Different types of f-divergence will result in different policies, which we call imitation modes. Furthermore, our approach enables the incorporation of spatial and temporal trajectory modulation, which is necessary for robots to be adaptive to the change in working conditions. We benchmark our algorithm against state-of-the-art methods in terms of trajectory reproduction and adaptation. The quantitative evaluation shows that our approach outperforms other algorithms regarding both accuracy and efficiency. We also report real-world experimental results on learning manifold trajectories in a polishing task with a KUKA LWR robot arm, illustrating the effectiveness of our algorithmic framework.

Real-Time Motion Planning for In-Hand Manipulation with a Multi-Fingered Hand

Dexterous manipulation of objects once held in hand remains a challenge. Such skills are, however, necessary for robotics to move beyond gripper-based manipulation and use all the dexterity offered by anthropomorphic robotic hands. One major challenge when manipulating an object within the hand is that fingers must move around the object while avoiding collision with other fingers or the object. Such collision-free paths must be computed in real-time, as the smallest deviation from the original plan can easily lead to collisions. We present a real-time approach to computing collision-free paths in a high-dimensional space. To guide the exploration, we learn an explicit representation of the free space, retrievable in real-time. We further combine this representation with closed-loop control via dynamical systems and sampling-based motion planning and show that the combination increases performance compared to alternatives, offering efficient search of feasible paths and real-time obstacle avoidance in a multi-fingered robotic hand.

Avoidance of Concave Obstacles through Rotation of Nonlinear Dynamics

Controlling complex tasks in robotic systems, such as circular motion for cleaning or following curvy lines, can be dealt with using nonlinear vector fields. In this paper, we introduce a novel approach called rotational obstacle avoidance method (ROAM) for adapting the initial dynamics when the workspace is partially occluded by obstacles. ROAM presents a closed-form solution that effectively avoids star-shaped obstacles in spaces of arbitrary dimensions by rotating the initial dynamics towards the tangent space. The algorithm enables navigation within obstacle hulls and can be customized to actively move away from surfaces, while guaranteeing the presence of only a single saddle point on the boundary of each obstacle. We introduce a sequence of mappings to extend the approach for general nonlinear dynamics. Moreover, ROAM extends its capabilities to handle multi-obstacle environments and provides the ability to constrain dynamics within a safe tube. By utilizing weighted vector-tree summation, we successfully navigate around general concave obstacles represented as a tree-of-stars. Through experimental evaluation, ROAM demonstrates superior performance in terms of minimizing occurrences of local minima and maintaining similarity to the initial dynamics, outperforming existing approaches in multi-obstacle simulations. The proposed method is highly reactive, owing to its simplicity, and can be applied effectively in dynamic environments. This was demonstrated during the collision-free navigation of a 7 degree-of-freedom robot arm around dynamic obstacles

Exploiting Kinematic Redundancy for Robotic Grasping of Multiple Objects

Humans coordinate the abundant degrees of freedom (DoFs) of hands to dexterously perform tasks in everyday life. We imitate human strategies to advance the dexterity of multi-DoF robotic hands. Specifically, we enable a robot hand to grasp multiple objects by exploiting its kinematic redundancy, referring to all its controllable DoFs. We propose a human-like grasp synthesis algorithm to generate grasps using pairwise contacts on arbitrary opposing hand surface regions, no longer limited to fingertips or hand inner surface. To model the available space of the hand for grasp, we construct a reachability map, consisting of reachable spaces of all finger phalanges and the palm. It guides the formulation of a constrained optimization problem, solving for feasible and stable grasps. We formulate an iterative process to empower robotic hands to grasp multiple objects in sequence. Moreover, we propose a kinematic efficiency metric and an associated strategy to facilitate exploiting kinematic redundancy. We validated our approaches by generating grasps of single and multiple objects using various hand surface regions. Such grasps can be successfully replicated on a real robotic hand.

From Obstacle Avoidance To Motion Learning Using Local Rotation of Dynamical Systems

In robotics motion is often described from an external perspective, i.e., we give information on the obstacle motion in a mathematical manner with respect to a specific (often inertial) reference frame. In the current work, we propose to describe the robotic motion with respect to the robot itself. Similar to how we give instructions to each other (go straight, and then after multiple meters move left, and then a sharp turn right.), we give the instructions to a robot as a relative rotation. We first introduce an obstacle avoidance framework that allows avoiding star-shaped obstacles while trying to stay close to an initial (linear or nonlinear) dynamical system. The framework of the local rotation is extended to motion learning. Automated clustering defines regions of local stability, for which the precise dynamics are individually learned. The framework has been applied to the LASA-handwriting dataset and shows promising results.