Hamilton-Jacobi Reachability Analysis for Hybrid Systems with Controlled and Forced Transitions

Hybrid dynamical systems with non-linear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of such hybrid systems can still prove to be a challenging problem because it requires simultaneous reasoning about continuous state evolution and discrete mode switching. In this work, we address this problem by extending classical Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for continuous non-linear dynamics in the presence of bounded inputs and disturbances, to hybrid dynamical systems. Our framework can compute reachable sets for hybrid systems consisting of multiple discrete modes, each with its own set of non-linear continuous dynamics, discrete transitions that can be directly commanded or forced by a discrete control input, while still accounting for control bounds and adversarial disturbances in the state evolution. Along with the reachable set, the proposed framework also provides an optimal continuous and discrete controller to ensure system safety. We demonstrate our framework in simulation on an aircraft collision avoidance problem, as well as on a real-world testbed to solve the optimal mode planning problem for a quadruped with multiple gaits.

Segmenting mechanically heterogeneous domains via unsupervised learning

From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous deformations with or without underlying material heterogeneity. Many recent works have established that computational modeling approaches are well suited for understanding and predicting the consequences of material heterogeneity and for interpreting observed heterogeneous strain fields. In particular, there has been significant work towards developing inverse analysis approaches that can convert observed kinematic quantities (e.g., displacement, strain) to material properties and mechanical state. Despite the success of these approaches, they are not necessarily generalizable and often rely on tight control and knowledge of boundary conditions. Here, we will build on the recent advances (and ubiquity) of machine learning approaches to explore alternative approaches to detect patterns in heterogeneous material properties and mechanical behavior. Specifically, we will explore unsupervised learning approaches to clustering and ensemble clutering to identify heterogeneous regions. Overall, we find that these approaches are effective, yet limited in their abilities. Through this initial exploration (where all data and code is published alongside this manuscript), we set the stage for future studies that more specifically adapt these methods to mechanical data.

Adaptive Force-Based Control of Dynamic Legged Locomotion over Uneven Terrain

Agile-legged robots have proven to be highly effective in navigating and performing tasks in complex and challenging environments, including disaster zones and industrial settings. However, these applications normally require the capability of carrying heavy loads while maintaining dynamic motion. Therefore, this paper presents a novel methodology for incorporating adaptive control into a force-based control system. Recent advancements in the control of quadruped robots show that force control can effectively realize dynamic locomotion over rough terrain. By integrating adaptive control into the force-based controller, our proposed approach can maintain the advantages of the baseline framework while adapting to significant model uncertainties and unknown terrain impact models. Experimental validation was successfully conducted on the Unitree A1 robot. With our approach, the robot can carry heavy loads (up to 50% of its weight) while performing dynamic gaits such as fast trotting and bounding across uneven terrains.

Cross-Institutional Transfer Learning for Educational Models: Implications for Model Performance, Fairness, and Equity

Modern machine learning increasingly supports paradigms that are multi-institutional (using data from multiple institutions during training) or cross-institutional (using models from multiple institutions for inference), but the empirical effects of these paradigms are not well understood. This study investigates cross-institutional learning via an empirical case study in higher education. We propose a framework and metrics for assessing the utility and fairness of student dropout prediction models that are transferred across institutions. We examine the feasibility of cross-institutional transfer under real-world data- and model-sharing constraints, quantifying model biases for intersectional student identities, characterizing potential disparate impact due to these biases, and investigating the impact of various cross-institutional ensembling approaches on fairness and overall model performance. We perform this analysis on data representing over 200,000 enrolled students annually from four universities without sharing training data between institutions. We find that a simple zero-shot cross-institutional transfer procedure can achieve similar performance to locally-trained models for all institutions in our study, without sacrificing model fairness. We also find that stacked ensembling provides no additional benefits to overall performance or fairness compared to either a local model or the zero-shot transfer procedure we tested. We find no evidence of a fairness-accuracy tradeoff across dozens of models and transfer schemes evaluated. Our auditing procedure also highlights the importance of intersectional fairness analysis, revealing performance disparities at the intersection of sensitive identity groups that are concealed under one-dimensional analysis.

Hierarchical Adaptive Control for Collaborative Manipulation of a Rigid Object by Quadrupedal Robots

Despite the potential benefits of collaborative robots, effective manipulation tasks with quadruped robots remain difficult to realize. In this paper, we propose a hierarchical control system that can handle real-world collaborative manipulation tasks, including uncertainties arising from object properties, shape, and terrain. Our approach consists of three levels of controllers. Firstly, an adaptive controller computes the required force and moment for object manipulation without prior knowledge of the object's properties and terrain. The computed force and moment are then optimally distributed between the team of quadruped robots using a Quadratic Programming (QP)-based controller. This QP-based controller optimizes each robot's contact point location with the object while satisfying constraints associated with robot-object contact. Finally, a decentralized loco-manipulation controller is designed for each robot to apply manipulation force while maintaining the robot's stability. We successfully validated our approach in a high-fidelity simulation environment where a team of quadruped robots manipulated an unknown object weighing up to 18 kg on different terrains while following the desired trajectory.

Learning Multimodal Bipedal Locomotion and Implicit Transitions: A Versatile Policy Approach

In this paper, we propose a novel framework for synthesizing a single multimodal control policy capable of generating diverse behaviors (or modes) and emergent inherent transition maneuvers for bipedal locomotion. In our method, we first learn efficient latent encodings for each behavior by training an autoencoder from a dataset of rough reference motions. These latent encodings are used as commands to train a multimodal policy through an adaptive sampling of modes and transitions to ensure consistent performance across different behaviors. We validate the policy performance in simulation for various distinct locomotion modes such as walking, leaping, jumping on a block, standing idle, and all possible combinations of inter-mode transitions. Finally, we integrate a task-based planner to rapidly generate open-loop mode plans for the trained multimodal policy to solve high-level tasks like reaching a goal position on a challenging terrain. Complex parkour-like motions by smoothly combining the discrete locomotion modes were generated in 3 min. to traverse tracks with a gap of width 0.45 m, a plateau of height 0.2 m, and a block of height 0.4 m, which are all significant compared to the dimensions of our mini-biped platform.

Kinodynamics-based Pose Optimization for Humanoid Loco-manipulation

This paper presents a novel approach for controlling humanoid robots pushing heavy objects using kinodynamics-based pose optimization and loco-manipulation MPC. The proposed pose optimization plans the optimal pushing pose for the robot while accounting for the unified object-robot dynamics model in steady state, robot kinematic constraints, and object parameters. The approach is combined with loco-manipulation MPC to track the optimal pose. Coordinating pushing reaction forces and ground reaction forces, the MPC allows accurate tracking in manipulation while maintaining stable locomotion. In numerical validation, the framework enables the humanoid robot to effectively push objects with a variety of parameter setups. The pose optimization generates different pushing poses for each setup and can be efficiently solved as a nonlinear programming (NLP) problem, averaging 250 ms. The proposed control scheme enables the humanoid robot to push object with a mass of up to 20 kg (118$\%$ of the robot's mass). Additionally, the MPC can recover the system when a 120 N force disturbance is applied to the object.

Adversarial Online Multi-Task Reinforcement Learning

We consider the adversarial online multi-task reinforcement learning setting, where in each of $K$ episodes the learner is given an unknown task taken from a finite set of $M$ unknown finite-horizon MDP models. The learner's objective is to minimize its regret with respect to the optimal policy for each task. We assume the MDPs in $\mathcal{M}$ are well-separated under a notion of $\lambda$-separability, and show that this notion generalizes many task-separability notions from previous works. We prove a minimax lower bound of $\Omega(K\sqrt{DSAH})$ on the regret of any learning algorithm and an instance-specific lower bound of $\Omega(\frac{K}{\lambda^2})$ in sample complexity for a class of uniformly-good cluster-then-learn algorithms. We use a novel construction called 2-JAO MDP for proving the instance-specific lower bound. The lower bounds are complemented with a polynomial time algorithm that obtains $\tilde{O}(\frac{K}{\lambda^2})$ sample complexity guarantee for the clustering phase and $\tilde{O}(\sqrt{MK})$ regret guarantee for the learning phase, indicating that the dependency on $K$ and $\frac{1}{\lambda^2}$ is tight.

FedDCT: Federated Learning of Large Convolutional Neural Networks on Resource Constrained Devices using Divide and Co-Training

We introduce FedDCT, a novel distributed learning paradigm that enables the usage of large, high-performance CNNs on resource-limited edge devices. As opposed to traditional FL approaches, which require each client to train the full-size neural network independently during each training round, the proposed FedDCT allows a cluster of several clients to collaboratively train a large deep learning model by dividing it into an ensemble of several small sub-models and train them on multiple devices in parallel while maintaining privacy. In this co-training process, clients from the same cluster can also learn from each other, further improving their ensemble performance. In the aggregation stage, the server takes a weighted average of all the ensemble models trained by all the clusters. FedDCT reduces the memory requirements and allows low-end devices to participate in FL. We empirically conduct extensive experiments on standardized datasets, including CIFAR-10, CIFAR-100, and two real-world medical datasets HAM10000 and VAIPE. Experimental results show that FedDCT outperforms a set of current SOTA FL methods with interesting convergence behaviors. Furthermore, compared to other existing approaches, FedDCT achieves higher accuracy and substantially reduces the number of communication rounds (with $4-8$ times fewer memory requirements) to achieve the desired accuracy on the testing dataset without incurring any extra training cost on the server side.

Contact Optimization for Non-Prehensile Loco-Manipulation via Hierarchical Model Predictive Control

Recent studies on quadruped robots have focused on either locomotion or mobile manipulation using a robotic arm. Legged robots can manipulate heavier and larger objects using non-prehensile manipulation primitives, such as planar pushing, to drive the object to the desired location. In this paper, we present a novel hierarchical model predictive control (MPC) for contact optimization of the manipulation task. Using two cascading MPCs, we split the loco-manipulation problem into two parts: the first to optimize both contact force and contact location between the robot and the object, and the second to regulate the desired interaction force through the robot locomotion. Our method is successfully validated in both simulation and hardware experiments. While the baseline locomotion MPC fails to follow the desired trajectory of the object, our proposed approach can effectively control both object's position and orientation with minimal tracking error. This capability also allows us to perform obstacle avoidance for both the robot and the object during the loco-manipulation task.