A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control

In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation.

AdvMT: Adversarial Motion Transformer for Long-term Human Motion Prediction

To achieve seamless collaboration between robots and humans in a shared environment, accurately predicting future human movements is essential. Human motion prediction has traditionally been approached as a sequence prediction problem, leveraging historical human motion data to estimate future poses. Beginning with vanilla recurrent networks, the research community has investigated a variety of methods for learning human motion dynamics, encompassing graph-based and generative approaches. Despite these efforts, achieving accurate long-term predictions continues to be a significant challenge. In this regard, we present the Adversarial Motion Transformer (AdvMT), a novel model that integrates a transformer-based motion encoder and a temporal continuity discriminator. This combination effectively captures spatial and temporal dependencies simultaneously within frames. With adversarial training, our method effectively reduces the unwanted artifacts in predictions, thereby ensuring the learning of more realistic and fluid human motions. The evaluation results indicate that AdvMT greatly enhances the accuracy of long-term predictions while also delivering robust short-term predictions

Clustering Techniques for Stable Linear Dynamical Systems with applications to Hard Disk Drives

In Robust Control and Data Driven Robust Control design methodologies, multiple plant transfer functions or a family of transfer functions are considered and a common controller is designed such that all the plants that fall into this family are stabilized. Though the plants are stabilized, the controller might be sub-optimal for each of the plants when the variations in the plants are large. This paper presents a way of clustering stable linear dynamical systems for the design of robust controllers within each of the clusters such that the controllers are optimal for each of the clusters. First a k-medoids algorithm for hard clustering will be presented for stable Linear Time Invariant (LTI) systems and then a Gaussian Mixture Models (GMM) clustering for a special class of LTI systems, common for Hard Disk Drive plants, will be presented.

Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planning

Diffusion models have risen as a powerful tool in robotics due to their flexibility and multi-modality. While some of these methods effectively address complex problems, they often depend heavily on inference-time obstacle detection and require additional equipment. Addressing these challenges, we present a method that, during inference time, simultaneously generates only reachable goals and plans motions that avoid obstacles, all from a single visual input. Central to our approach is the novel use of a collision-avoiding diffusion kernel for training. Through evaluations against behavior-cloning and classical diffusion models, our framework has proven its robustness. It is particularly effective in multi-modal environments, navigating toward goals and avoiding unreachable ones blocked by obstacles, while ensuring collision avoidance.

Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation

Recent studies have verified that equivariant methods can significantly improve the data efficiency, generalizability, and robustness in robot learning. Meanwhile, denoising diffusion-based generative modeling has recently gained significant attention as a promising approach for robotic manipulation learning from demonstrations with stochastic behaviors. In this paper, we present Diffusion-EDFs, a novel approach that incorporates spatial roto-translation equivariance, i.e., SE(3)-equivariance to diffusion generative modeling. By integrating SE(3)-equivariance into our model architectures, we demonstrate that our proposed method exhibits remarkable data efficiency, requiring only 5 to 10 task demonstrations for effective end-to-end training. Furthermore, our approach showcases superior generalizability compared to previous diffusion-based manipulation methods.

Robot Manipulation Task Learning by Leveraging SE(3) Group Invariance and Equivariance

This paper presents a differential geometric control approach that leverages SE(3) group invariance and equivariance to increase transferability in learning robot manipulation tasks that involve interaction with the environment. Specifically, we employ a control law and a learning representation framework that remain invariant under arbitrary SE(3) transformations of the manipulation task definition. Furthermore, the control law and learning representation framework are shown to be SE(3) equivariant when represented relative to the spatial frame. The proposed approach is based on utilizing a recently presented geometric impedance control (GIC) combined with a learning variable impedance control framework, where the gain scheduling policy is trained in a supervised learning fashion from expert demonstrations. A geometrically consistent error vector (GCEV) is fed to a neural network to achieve a gain scheduling policy that remains invariant to arbitrary translation and rotations. A comparison of our proposed control and learning framework with a well-known Cartesian space learning impedance control, equipped with a Cartesian error vector-based gain scheduling policy, confirms the significantly superior learning transferability of our proposed approach. A hardware implementation on a peg-in-hole task is conducted to validate the learning transferability and feasibility of the proposed approach.

Layered Cost-Map-Based Traffic Management for Multiple Automated Mobile Robots via a Data Distribution Service

This letter proposes traffic management for multiple automated mobile robots (AMRs) based on a layered cost map. Multiple AMRs communicate via a data distribution service (DDS), which is shared by topics in the same DDS domain. The cost of each layer is manipulated by topics. The traffic management server in the domain sends or receives topics to each of AMRs. Using the layered cost map, the new concept of prohibition filter, lane filter, fleet layer, and region filter are proposed and implemented. The prohibition filter can help a user set an area that would prohibit an AMR from trespassing. The lane filter can help set one-way directions based on an angle image. The fleet layer can help AMRs share their locations via the traffic management server. The region filter requests for or receives an exclusive area, which can be occupied by only one AMR, from the traffic management server. All the layers are experimentally validated with real-world AMRs. Each area can be configured with user-defined images or text-based parameter files.

Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning

End-to-end learning for visual robotic manipulation is known to suffer from sample inefficiency, requiring a large number of demonstrations. The spatial roto-translation equivariance, or the SE(3)-equivariance can be exploited to improve the sample efficiency for learning robotic manipulation. In this paper, we present fully end-to-end SE(3)-equivariant models for visual robotic manipulation from a point cloud input. By utilizing the representation theory of the Lie group, we construct novel SE(3)-equivariant energy-based models that allow highly sample efficient end-to-end learning. We show that our models can learn from scratch without prior knowledge yet is highly sample efficient (~10 demonstrations are enough). Furthermore, we show that the trained models can generalize to tasks with (i) previously unseen target object poses, (ii) previously unseen target object instances of the category, and (iii) previously unseen visual distractors. We experiment with 6-DoF robotic manipulation tasks to validate our models' sample efficiency and generalizability. Codes are available at: https://github.com/tomato1mule/edf

Behavior Tree-Based Asynchronous Task Planning for Multiple Mobile Robots using a Data Distribution Service

In this study, we propose task planning framework for multiple robots that builds on a behavior tree (BT). BTs communicate with a data distribution service (DDS) to send and receive data. Since the standard BT derived from one root node with a single tick is unsuitable for multiple robots, a novel type of BT action and improved nodes are proposed to control multiple robots through a DDS asynchronously. To plan tasks for robots efficiently, a single task planning unit is implemented with the proposed task types. The task planning unit assigns tasks to each robot simultaneously through a single coalesced BT. If any robot falls into a fault while performing its assigned task, another BT embedded in the robot is executed; the robot enters the recovery mode in order to overcome the fault. To perform this function, the action in the BT corresponding to the task is defined as a variable, which is shared with the DDS so that any action can be exchanged between the task planning unit and robots. To show the feasibility of our framework in a real-world application, three mobile robots were experimentally coordinated for them to travel alternately to four goal positions by the proposed single task planning unit via a DDS.

Attaining Interpretability in Reinforcement Learning via Hierarchical Primitive Composition

Deep reinforcement learning has shown its effectiveness in various applications and provides a promising direction for solving tasks with high complexity. In most reinforcement learning algorithms, however, two major issues need to be dealt with - the sample inefficiency and the interpretability of a policy. The former happens when the environment is sparsely rewarded and/or has a long-term credit assignment problem, while the latter becomes a problem when the learned policies are deployed at the customer side product. In this paper, we propose a novel hierarchical reinforcement learning algorithm that mitigates the aforementioned issues by decomposing the original task in a hierarchy and by compounding pretrained primitives with intents. We show how the proposed scheme can be employed in practice by solving a pick and place task with a 6 DoF manipulator.