Safe and Stable Teleoperation of Quadrotor UAVs under Haptic Shared Autonomy

We present a novel approach that aims to address both safety and stability of a haptic teleoperation system within a framework of Haptic Shared Autonomy (HSA). We use Control Barrier Functions (CBFs) to generate the control input that follows the user's input as closely as possible while guaranteeing safety. In the context of stability of the human-in-the-loop system, we limit the force feedback perceived by the user via a small $L_2$-gain, which is achieved by limiting the control and the force feedback via a differential constraint. Specifically, with the property of HSA, we propose two pathways to design the control and the force feedback: Sequential Control Force (SCF) and Joint Control Force (JCF). Both designs can achieve safety and stability but with different responses to the user's commands. We conducted experimental simulations to evaluate and investigate the properties of the designed methods. We also tested the proposed method on a physical quadrotor UAV and a haptic interface.

Enhancing Security in Multi-Robot Systems through Co-Observation Planning, Reachability Analysis, and Network Flow

This paper addresses security challenges in multi-robot systems (MRS) where adversaries may compromise robot control, risking unauthorized access to forbidden areas. We propose a novel multi-robot optimal planning algorithm that integrates mutual observations and introduces reachability constraints for enhanced security. This ensures that, even with adversarial movements, compromised robots cannot breach forbidden regions without missing scheduled co-observations. The reachability constraint uses ellipsoidal over-approximation for efficient intersection checking and gradient computation. To enhance system resilience and tackle feasibility challenges, we also introduce sub-teams. These cohesive units replace individual robot assignments along each route, enabling redundant robots to deviate for co-observations across different trajectories, securing multiple sub-teams without requiring modifications. We formulate the cross-trajectory co-observation plan by solving a network flow coverage problem on the checkpoint graph generated from the original unsecured MRS trajectories, providing the same security guarantees against plan-deviation attacks. We demonstrate the effectiveness and robustness of our proposed algorithm, which significantly strengthens the security of multi-robot systems in the face of adversarial threats.

IKSPARK: An Inverse Kinematics Solver using Semidefinite Relaxation and Rank Minimization

Inverse kinematics (IK) is a fundamental problem frequently occurred in robot control and motion planning. However, the problem is nonconvex because the kinematic map between the configuration and task spaces is generally nonlinear, which makes it challenging for fast and accurate solutions. The problem can be more complicated with the existence of different physical constraints imposed by the robot structure. In this paper, we develop an inverse kinematics solver named IKSPARK (Inverse Kinematics using Semidefinite Programming And RanK minimization) that can find solutions for robots with various structures, including open/closed kinematic chains, spherical, revolute, and/or prismatic joints. The solver works in the space of rotation matrices of the link reference frames and involves solving only convex semidefinite problems (SDPs). Specifically, the IK problem is formulated as an SDP with an additional rank-1 constraint on symmetric matrices with constant traces. The solver first solves this SDP disregarding the rank constraint to get a start point and then finds the rank-1 solution iteratively via a rank minimization algorithm with proven local convergence. Compared to other work that performs SDP relaxation for IK problems, our formulation is simpler, and uses variables with smaller sizes. We validate our approach via simulations on different robots, comparing against a standard IK method.

Multi-class Temporal Logic Neural Networks

Time-series data can represent the behaviors of autonomous systems, such as drones and self-driving cars. The problem of binary and multi-class classification has received a lot of attention in this field. Neural networks represent a popular approach to classifying data; However, they lack interpretability, which poses a significant challenge in extracting meaningful information from them. Signal Temporal Logic (STL) is a formalism to describe the properties of timed behaviors. We propose a method that combines all of the above: neural networks that represent STL specifications for multi-class classification of time-series data. We offer two key contributions: 1) We introduce a notion of margin for multi-class classification, and 2) we introduce the use of STL-based attributes for enhancing the interpretability of the results. We evaluate our method on two datasets and compare with state-of-the-art baselines.

Interpretable Generative Adversarial Imitation Learning

Imitation learning methods have demonstrated considerable success in teaching autonomous systems complex tasks through expert demonstrations. However, a limitation of these methods is their lack of interpretability, particularly in understanding the specific task the learning agent aims to accomplish. In this paper, we propose a novel imitation learning method that combines Signal Temporal Logic (STL) inference and control synthesis, enabling the explicit representation of the task as an STL formula. This approach not only provides a clear understanding of the task but also allows for the incorporation of human knowledge and adaptation to new scenarios through manual adjustments of the STL formulae. Additionally, we employ a Generative Adversarial Network (GAN)-inspired training approach for both the inference and the control policy, effectively narrowing the gap between the expert and learned policies. The effectiveness of our algorithm is demonstrated through two case studies, showcasing its practical applicability and adaptability.

Efficient LQR-CBF-RRT*: Safe and Optimal Motion Planning

Control Barrier Functions (CBF) are a powerful tool for designing safety-critical controllers and motion planners. The safety requirements are encoded as a continuously differentiable function that maps from state variables to a real value, in which the sign of its output determines whether safety is violated. In practice, the CBFs can be used to enforce safety by imposing itself as a constraint in a Quadratic Program (QP) solved point-wise in time. However, this approach costs computational resources and could lead to infeasibility in solving the QP. In this paper, we propose a novel motion planning framework that combines sampling-based methods with Linear Quadratic Regulator (LQR) and CBFs. Our approach does not require solving the QPs for control synthesis and avoids explicit collision checking during samplings. Instead, it uses LQR to generate optimal controls and CBF to reject unsafe trajectories. To improve sampling efficiency, we employ the Cross-Entropy Method (CEM) for importance sampling (IS) to sample configurations that will enhance the path with higher probability and store computed optimal gain matrices in a hash table to avoid re-computation during rewiring procedure. We demonstrate the effectiveness of our method on nonlinear control affine systems in simulation.

Byzantine Resilience at Swarm Scale: A Decentralized Blocklist Protocol from Inter-robot Accusations

The Weighted-Mean Subsequence Reduced (W-MSR) algorithm, the state-of-the-art method for Byzantine-resilient design of decentralized multi-robot systems, is based on discarding outliers received over Linear Consensus Protocol (LCP). Although W-MSR provides well-understood theoretical guarantees relating robust network connectivity to the convergence of the underlying consensus, the method comes with several limitations preventing its use at scale: (1) the number of Byzantine robots, F, to tolerate should be known a priori, (2) the requirement that each robot maintains 2F+1 neighbors is impractical for large F, (3) information propagation is hindered by the requirement that F+1 robots independently make local measurements of the consensus property in order for the swarm's decision to change, and (4) W-MSR is specific to LCP and does not generalize to applications not implemented over LCP. In this work, we propose a Decentralized Blocklist Protocol (DBP) based on inter-robot accusations. Accusations are made on the basis of locally-made observations of misbehavior, and once shared by cooperative robots across the network are used as input to a graph matching algorithm that computes a blocklist. DBP generalizes to applications not implemented via LCP, is adaptive to the number of Byzantine robots, and allows for fast information propagation through the multi-robot system while simultaneously reducing the required network connectivity relative to W-MSR. On LCP-type applications, DBP reduces the worst-case connectivity requirement of W-MSR from (2F+1)-connected to (F+1)-connected and the number of cooperative observers required to propagate new information from F+1 to just 1 observer. We demonstrate empirically that our approach to Byzantine resilience scales to hundreds of robots on cooperative target tracking, time synchronization, and localization case studies.

A Graph-Based Approach to Generate Energy-Optimal Robot Trajectories in Polygonal Environments

As robotic systems continue to address emerging issues in areas such as logistics, mobility, manufacturing, and disaster response, it is increasingly important to rapidly generate safe and energy-efficient trajectories. In this article, we present a new approach to plan energy-optimal trajectories through cluttered environments containing polygonal obstacles. In particular, we develop a method to quickly generate optimal trajectories for a double-integrator system, and we show that optimal path planning reduces to an integer program. To find an efficient solution, we present a distance-informed prefix search to efficiently generate optimal trajectories for a large class of environments. We demonstrate that our approach, while matching the performance of RRT* and Probabilistic Road Maps in terms of path length, outperforms both in terms of energy cost and computational time by up to an order of magnitude. We also demonstrate that our approach yields implementable trajectories in an experiment with a Crazyflie quadrotor.

A Graph-Based Approach to Generate Energy-Optimal Robot Trajectories in Polynomial Environments

As robotic systems continue to address emerging issues in areas such as logistics, mobility, manufacturing, and disaster response, it is increasingly important to rapidly generate safe and energy-efficient trajectories. In this article, we present a new approach to plan energy-optimal trajectories through cluttered environments containing polygonal obstacles. In particular, we develop a method to quickly generate optimal trajectories for a double-integrator system, and we show that optimal path planning reduces to an integer program. To find an efficient solution, we present a distance-informed prefix search to efficiently generate optimal trajectories for a large class of environments. We demonstrate that our approach, while matching the performance of RRT* and Probabilistic Road Maps in terms of path length, outperforms both in terms of energy cost and computational time by up to an order of magnitude. We also demonstrate that our approach yields implementable trajectories in an experiment with a Crazyflie quadrotor.

Learning Signal Temporal Logic through Neural Network for Interpretable Classification

Machine learning techniques using neural networks have achieved promising success for time-series data classification. However, the models that they produce are challenging to verify and interpret. In this paper, we propose an explainable neural-symbolic framework for the classification of time-series behaviors. In particular, we use an expressive formal language, namely Signal Temporal Logic (STL), to constrain the search of the computation graph for a neural network. We design a novel time function and sparse softmax function to improve the soundness and precision of the neural-STL framework. As a result, we can efficiently learn a compact STL formula for the classification of time-series data through off-the-shelf gradient-based tools. We demonstrate the computational efficiency, compactness, and interpretability of the proposed method through driving scenarios and naval surveillance case studies, compared with state-of-the-art baselines.