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.

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.

Geometric Impedance Control on SE for Robotic Manipulators

After its introduction, impedance control has been utilized as a primary control scheme for robotic manipulation tasks that involve interaction with unknown environments. While impedance control has been extensively studied, the geometric structure of SE(3) for the robotic manipulator itself and its use in formulating a robotic task has not been adequately addressed. In this paper, we propose a differential geometric approach to impedance control. Given a left-invariant error metric in SE(3), the corresponding error vectors in position and velocity are first derived. Using these geometrically consistent error vectors, we propose a novel impedance control scheme, which adequately accounts for the geometric structure of the manipulator in SE(3). The closed-loop stability for the proposed control schemes is verified using a Lyapunov function-based analysis. The proposed control design clearly outperformed a conventional impedance control approach when tracking challenging trajectory profiles.

Attentional Policies for Cross-Context Multi-Agent Reinforcement Learning

Many potential applications of reinforcement learning in the real world involve interacting with other agents whose numbers vary over time. We propose new neural policy architectures for these multi-agent problems. In contrast to other methods of training an individual, discrete policy for each agent and then enforcing cooperation through some additional inter-policy mechanism, we follow the spirit of recent work on the power of relational inductive biases in deep networks by learning multi-agent relationships at the policy level via an attentional architecture. In our method, all agents share the same policy, but independently apply it in their own context to aggregate the other agents' state information when selecting their next action. The structure of our architectures allow them to be applied on environments with varying numbers of agents. We demonstrate our architecture on a benchmark multi-agent autonomous vehicle coordination problem, obtaining superior results to a full-knowledge, fully-centralized reference solution, and significantly outperforming it when scaling to large numbers of agents.

Neural-Attention-Based Deep Learning Architectures for Modeling Traffic Dynamics on Lane Graphs

Deep neural networks can be powerful tools, but require careful application-specific design to ensure that the most informative relationships in the data are learnable. In this paper, we apply deep neural networks to the nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We consider problems of estimating macroscopic quantities (e.g., the queue at an intersection) at a lane level. First-principles modeling at the lane scale has been a challenge due to complexities in modeling social behaviors like lane changes, and those behaviors' resultant macro-scale effects. Following domain knowledge that upstream/downstream lanes and neighboring lanes affect each others' traffic flows in distinct ways, we apply a form of neural attention that allows the neural network layers to aggregate information from different lanes in different manners. Using a microscopic traffic simulator as a testbed, we obtain results showing that an attentional neural network model can use information from nearby lanes to improve predictions, and, that explicitly encoding the lane-to-lane relationship types significantly improves performance. We also demonstrate the transfer of our learned neural network to a more complex road network, discuss how its performance degradation may be attributable to new traffic behaviors induced by increased topological complexity, and motivate learning dynamics models from many road network topologies.

Vehicle Localization and Control on Roads with Prior Grade Map

We propose a map-aided vehicle localization method for GPS-denied environments. This approach exploits prior knowledge of the road grade map and vehicle on-board sensor measurements to accurately estimate the longitudinal position of the vehicle. Real-time localization is crucial to systems that utilize position-dependent information for planning and control. We validate the effectiveness of the localization method on a hierarchical control system. The higher level planner optimizes the vehicle velocity to minimize the energy consumption for a given route by employing traffic condition and road grade data. The lower level is a cruise control system that tracks the position-dependent optimal reference velocity. Performance of the proposed localization algorithm is evaluated using both simulations and experiments.