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This paper considers how heterogeneous multi-agent teams can leverage their different capabilities to mutually improve individual agent performance. We present Capability-Augmenting Tasks (CATs), which encode how agents can augment their capabilities based on interactions with other teammates. Our framework integrates CAT into the semantics of Metric Temporal Logic (MTL), which defines individual spatio-temporal tasks for all agents. A centralized Mixed-Integer Program (MIP) is used to synthesize trajectories for all agents. We compare the expressivity of our approach to a baseline of Capability Temporal Logic Plus (CaTL+). Case studies demonstrate that our approach allows for simpler specifications and improves individual performance when agents leverage the capabilities of their teammates.

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were developed to ensure stability, while adhering to input constraints and safety-critical requirements. This was achieved by incorporating discrete-time Control Barrier Functions (CBFs) within a Model Predictive Control (MPC) framework. Existing work usually centers on the feasibility or safety of optimization problems when the boundaries of safe sets are clearly defined. Most of this research limits discussions to CBFs with relative degree one with respect to the system dynamics. Furthermore, real-time computation becomes challenging in MPC problems with large horizons. In this paper, we introduce a framework that addresses the safety-critical MPC problem through iterative optimization, applicable across CBFs of any relative degree. Our approach involves linearizing the nonlinear system dynamics and safety constraints, modeled as Discrete-time High-Order CBFs (DHOCBFs), at each time step. Additionally, when the boundaries of the safe sets are complex, we present a learning-based method to develop linear boundary equations for these safe sets. These equations are then converted into linearized DHOCBFs. The benefits of computational performance and safe avoidance of obstacles with diverse shapes are examined and confirmed through numerical results., Comment: 16 pages, 12 figures. arXiv admin note: text overlap with arXiv:2210.04361

This paper presents a control framework for magnetically actuated cellbots, which combines Model Predictive Control (MPC) with Gaussian Processes (GPs) as a disturbance estimator for precise trajectory tracking. To address the challenges posed by unmodeled dynamics, we integrate data-driven modeling with model-based control to accurately track desired trajectories using relatively small data. To the best of our knowledge, this is the first work to integrate data-driven modeling with model-based control for the magnetic actuation of cellbots. The GP effectively learns and predicts unmodeled disturbances, providing uncertainty bounds as well. We validate our method through experiments with cellbots, demonstrating improved trajectory tracking accuracy.

Recent work has shown that stabilizing an affine control system while optimizing a quadratic cost subject to state and control constraints can be mapped to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this method is that the QPs could easily become infeasible under safety and spatio-temporal constraints with tight control bounds. In our own recent work, we defined Auxiliary-Variable Adaptive CBFs (AVCBFs) to improve the feasibility of the CBF-based QP, while avoiding extensive parameter tuning. In this paper, we consider spatio-temporal constraints as finite-time reachability requirements. In order to satisfy these requirements, we generalize AVCBFs to Auxiliary-Variable Adaptive Control Lyapunov Barrier Functions (AVCLBFs) that work for systems and constraints with arbitrary relative degrees. We show that our method has fewer conflicts with safety and input constraints, and outperforms the state of the art in term of adaptivity and feasibility in solving the QP. We illustrate our approach on an optimal control problem for a unicycle., Comment: 8 pages, 4 figures. arXiv admin note: text overlap with arXiv:2310.00238

Dynamic obstacle avoidance is a challenging topic for optimal control and optimization-based trajectory planning problems. Many existing works use Control Barrier Functions (CBFs) to enforce safety constraints for control systems. CBFs are typically formulated based on the distance to obstacles, or integrated with path planning algorithms as a safety enhancement tool. However, these approaches usually require knowledge of the obstacle boundary equations or have very slow computational efficiency. In this paper, we propose a framework based on model predictive control (MPC) with discrete-time high-order CBFs (DHOCBFs) to generate a collision-free trajectory. The DHOCBFs are first obtained from convex polytopes generated through grid mapping, without the need to know the boundary equations of obstacles. Additionally, a path planning algorithm is incorporated into this framework to ensure the global optimality of the generated trajectory. We demonstrate through numerical examples that our framework allows a unicycle robot to safely and efficiently navigate tight, dynamically changing environments with both convex and nonconvex obstacles. By comparing our method to established CBF-based benchmarks, we demonstrate superior computing efficiency, length optimality, and feasibility in trajectory generation and obstacle avoidance., Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:2210.04361

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., Comment: Submitted to L4DC 2024 (under review)

We propose an approach to synthesize linear feedback controllers for linear systems in polygonal environments. Our method focuses on designing a robust controller that can account for uncertainty in measurements. Its inputs are provided by a perception module that generates probability mass functions (PMFs) for predefined landmarks in the environment, such as distinguishable geometric features. We formulate an optimization problem with Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints to derive a stable and safe controller. Using the strong duality of linear programs (LPs) and robust optimization, we convert the optimization problem to a linear program that can be efficiently solved offline. At a high level, our approach partially combines perception, planning, and real-time control into a single design problem. An additional advantage of our method is the ability to produce controllers capable of exhibiting nonlinear behavior while relying solely on an offline LP for control synthesis.

This paper studies safety and feasibility guarantees for systems with tight control bounds. It has been shown that stabilizing an affine control system while optimizing a quadratic cost and satisfying state and control constraints can be mapped to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBF) and Control Lyapunov Functions (CLF). One of the main challenges in this method is that the QP could easily become infeasible under safety constraints of high relative degree, especially under tight control bounds. Recent work focused on deriving sufficient conditions for guaranteeing feasibility. The existing results are case-dependent. In this paper, we consider the general case. We define a feasibility constraint and propose a new type of CBF to enforce it. Our method guarantees the feasibility of the above mentioned QPs, while satisfying safety requirements. We demonstrate the proposed method on an Adaptive Cruise Control (ACC) problem for a heterogeneous platoon with tight control bounds, and compare our method to existing CBF-CLF approaches. The results show that our proposed approach can generate gradually transitioned control (without abrupt changes) with guaranteed feasibility and safety., Comment: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:2304.00372

Temporal logics (TLs) have been widely used to formalize interpretable tasks for cyber-physical systems. Time Window Temporal Logic (TWTL) has been recently proposed as a specification language for dynamical systems. In particular, it can easily express robotic tasks, and it allows for efficient, automata-based verification and synthesis of control policies for such systems. In this paper, we define two quantitative semantics for this logic, and two corresponding monitoring algorithms, which allow for real-time quantification of satisfaction of formulas by trajectories of discrete-time systems. We demonstrate the new semantics and their runtime monitors on numerical examples., Comment: Submitted to the 62nd IEEE Conference on Decision and Control (CDC2023)

In this paper, we consider the problem of learning a neural network controller for a system required to satisfy a Signal Temporal Logic (STL) specification. We exploit STL quantitative semantics to define a notion of robust satisfaction. Guaranteeing the correctness of a neural network controller, i.e., ensuring the satisfaction of the specification by the controlled system, is a difficult problem that received a lot of attention recently. We provide a general procedure to construct a set of trainable High Order Control Barrier Functions (HOCBFs) enforcing the satisfaction of formulas in a fragment of STL. We use the BarrierNet, implemented by a differentiable Quadratic Program (dQP) with HOCBF constraints, as the last layer of the neural network controller, to guarantee the satisfaction of the STL formulas. We train the HOCBFs together with other neural network parameters to further improve the robustness of the controller. Simulation results demonstrate that our approach ensures satisfaction and outperforms existing algorithms., Comment: Submitted to CDC 2023

In this paper, we present a framework for online parameter estimation and uncertainty quantification in the context of adaptive safety-critical control. The key insight enabling our approach is that the parameter estimate generated by the continuous-time recursive least squares (RLS) algorithm at any point in time is an affine transformation of the initial parameter estimate. This property allows for parameterizing such estimates using objects that are closed under affine transformation, such as zonotopes, and enables the efficient propagation of such set-based estimates as time progresses. We illustrate how such an approach facilitates the synthesis of safety-critical controllers for systems with parametric uncertainty and additive disturbances using control barrier functions, and demonstrate the utility of our approach through illustrative examples., Comment: To appear at the 2024 American Control Conference

We present LQR-CBF-RRT*, an incremental sampling-based algorithm for offline motion planning. Our framework leverages the strength of Control Barrier Functions (CBFs) and Linear Quadratic Regulators (LQR) to generate safety-critical and optimal trajectories for a robot with dynamics described by an affine control system. CBFs are used for safety guarantees, while LQRs are employed for optimal control synthesis during edge extensions. Popular CBF-based formulations for safety critical control require solving Quadratic Programs (QPs), which can be computationally expensive. Moreover, LQR-based controllers require repetitive applications of first-order Taylor approximations for nonlinear systems, which can also create an additional computational burden. To improve the motion planning efficiency, we verify the satisfaction of the CBF constraints directly in edge extension to avoid the burden of solving the QPs. We store computed optimal LQR gain matrices in a hash table to avoid re-computation during the local linearization of the rewiring procedure. Lastly, we utilize the Cross-Entropy Method for importance sampling to improve sampling efficiency. Our results show that the proposed planner surpasses its counterparts in computational efficiency and performs well in an experimental setup.

This paper studies safety guarantees for systems with time-varying control bounds. It has been shown that optimizing quadratic costs subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBFs). One of the main challenges in this method is that the CBF-based QP could easily become infeasible under tight control bounds, especially when the control bounds are time-varying. The recently proposed adaptive CBFs have addressed such infeasibility issues, but require extensive and non-trivial hyperparameter tuning for the CBF-based QP and may introduce overshooting control near the boundaries of safe sets. To address these issues, we propose a new type of adaptive CBFs called Auxiliary-Variable Adaptive CBFs (AVCBFs). Specifically, we introduce an auxiliary variable that multiplies each CBF itself, and define dynamics for the auxiliary variable to adapt it in constructing the corresponding CBF constraint. In this way, we can improve the feasibility of the CBF-based QP while avoiding extensive parameter tuning with non-overshooting control since the formulation is identical to classical CBF methods. We demonstrate the advantages of using AVCBFs and compare them with existing techniques on an Adaptive Cruise Control (ACC) problem with time-varying control bounds., Comment: 8 pages, 4 figures. arXiv admin note: text overlap with arXiv:2310.00238

It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In this paper, we employ machine learning techniques to ensure the feasibility of these QPs, which is a challenging problem, especially for high relative degree constraints where High Order CBFs (HOCBFs) are required. To this end, we propose a sampling-based learning approach to learn a new feasibility constraint for CBFs; this constraint is then enforced by another HOCBF added to the QPs. The accuracy of the learned feasibility constraint is recursively improved by a recurrent training algorithm. We demonstrate the advantages of the proposed learning approach to constrained optimal control problems with specific focus on a robot control problem and on autonomous driving in an unknown environment., Comment: 8 pages, to appear in ECC 2023

This paper presents an adaptive control approach for uncertain nonlinear systems subject to safety constraints that allows for modularity in the selection of the parameter estimation algorithm. Such modularity is achieved by unifying the concepts of input-to-state stability (ISS) and input-to-state safety (ISSf) via control Lyapunov functions (CLFs) and control barrier functions (CBFs), respectively. In particular, we propose a class of exponential ISS-CLFs and ISSf high order CBFs that can be combined with a general class of parameter estimation algorithms akin to those found in the literature on concurrent learning adaptive control. We demonstrate that the unification of ISS and ISSf in an adaptive control setting allows for maintaining a single set of parameter estimates for both the CLF and CBF that can be generated by a class of update laws satisfying a few general properties. The modularity of our approach is demonstrated via numerical examples by comparing performance in terms of stability and safety across different parameter estimation algorithms., Comment: To appear at the 2023 American Control Conference

In this paper, we propose a learning-based framework to simultaneously learn the communication and distributed control policies for a heterogeneous multi-agent system (MAS) under complex mission requirements from Capability Temporal Logic plus (CaTL+) specifications. Both policies are trained, implemented, and deployed using a novel neural network model called CatlNet. Taking advantage of the robustness measure of CaTL+, we train CatlNet centrally to maximize it where network parameters are shared among all agents, allowing CatlNet to scale to large teams easily. CatlNet can then be deployed distributedly. A plan repair algorithm is also introduced to guide CatlNet's training and improve both training efficiency and the overall performance of CatlNet. The CatlNet approach is tested in simulation and results show that, after training, CatlNet can steer the decentralized MAS system online to satisfy a CaTL+ specification with a high success rate.

Micron-scale robots ($\mu$bots) have recently shown great promise for emerging medical applications. Accurate controlling $\mu$bots, while critical to their successful deployment, is challenging. In this work, we consider the problem of tracking a reference trajectory using a $\mu$bot in the presence of disturbances and uncertainty. The disturbances primarily come from Brownian motion and other environmental phenomena, while the uncertainty originates from errors in the model parameters. We model the $\mu$bot as an uncertain unicycle that is controlled by a global magnetic field. To compensate for disturbances and uncertainties, we develop a nonlinear mismatch controller. We define the model mismatch error as the difference between our model's predicted velocity and the actual velocity of the $\mu$bot. We employ a Gaussian Process to learn the model mismatch error as a function of the applied control input. Then we use a least-squares minimization to select a control action that minimizes the difference between the actual velocity of the $\mu$bot and a reference velocity. We demonstrate the online performance of our joint learning and control algorithm in simulation, where our approach accurately learns the model mismatch and improves tracking performance. We also validate our approach in an experiment and show that certain error metrics are reduced by up to $40\%$., Comment: 8 pages, 9 figures

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as safety-critical requirements using discrete-time control barrier functions within a model predictive control (MPC) framework. Existing work usually focus on the feasibility or the safety for the optimization problem, and the majority of the existing work restrict the discussions to relative-degree one control barrier functions. Additionally, the real-time computation is challenging when a large horizon is considered in the MPC problem for relative-degree one or high-order control barrier functions. In this paper, we propose a framework that solves the safety-critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high-order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results., Comment: The open source code is added and the paper is accepted to American Control Conference (ACC) 2023 (8 pages)

We consider the problem of controlling a heterogeneous multi-agent system required to satisfy temporal logic requirements. Capability Temporal Logic (CaTL) was recently proposed to formalize such specifications for deploying a team of autonomous agents with different capabilities and cooperation requirements. In this paper, we extend CaTL to a new logic CaTL+, which is more expressive than CaTL and has semantics over a continuous workspace shared by all agents. We define two novel robustness metrics for CaTL+: the traditional robustness and the exponential robustness. The latter is sound, differentiable almost everywhere and eliminates masking, which is one of the main limitations of the traditional robustness metric. We formulate a control synthesis problem to maximize CaTL+ robustness and propose a two-step optimization method to solve this problem. Simulation results are included to illustrate the increased expressivity of CaTL+ and the efficacy of the proposed control synthesis approach., Comment: Accepted to ACC 2023

This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust control barrier functions (RCBF) and robust control Lyapunov functions (RCLF) that facilitate the synthesis of safety-critical controllers in the presence of parametric uncertainty using quadratic programming. Since the initial bounds on the system uncertainty may be highly conservative, we present a data-driven approach to reducing such bounds using input-output data collected online. In particular, we leverage an integral set-membership identification algorithm that iteratively shrinks the set of possible system parameters online and guarantees stability and safety during learning. The efficacy of the developed approach is illustrated on two numerical examples., Comment: To appear at the 2022 IEEE Conference on Decision and Control

We take a divide and conquer approach to design controllers for reachability problems given large-scale linear systems with polyhedral constraints on states, controls, and disturbances. Such systems are made of small subsystems with coupled dynamics. We treat the couplings as additional disturbances and use assume-guarantee (AG) contracts to characterize these disturbance sets. For each subsystem, we design and implement a robust controller locally, subject to its own constraints and contracts. The main contribution of this paper is a method to derive the contracts via a novel parameterization and a corresponding potential function that characterizes the distance to the correct composition of controllers and contracts, where all contracts are held. We show that the potential function is convex in the contract parameters. This enables the subsystems to negotiate the contracts with the gradient information from the dual of their local synthesis optimization problems in a distributed way, facilitating compositional control synthesis that scales to large systems. We present numerical examples, including a scalability study on a system with tens of thousands of dimensions, and a case study on applying our method to a distributed Model Predictive Control (MPC) problem in a power system.

We develop a novel decentralized control method for a network of perturbed linear systems with dynamical couplings subject to Signal Temporal Logic (STL) specifications. We first transform the STL requirements into set containment problems and then we develop controllers to solve these problems. Our approach is based on treating the couplings between subsystems as disturbances, which are bounded sets that the subsystems negotiate in the form of parametric assume-guarantee contracts. The set containment requirements and parameterized contracts are added to the subsystems' constraints. We introduce a centralized optimization problem to derive the contracts, reachability tubes, and decentralized closed-loop control laws. We show that, when the STL formula is separable with respect to the subsystems, the centralized optimization problem can be solved in a distributed way, which scales to large systems. We present formal theoretical guarantees on robustness of STL satisfaction. The effectiveness of the proposed method is demonstrated via a power network case study.

Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for safety-critical systems. In this paper, we combine the effectiveness of RRT-based algorithms with the safety guarantees provided by CBFs in a method called CBF-RRT$^\ast$. CBFs are used for local trajectory planning for RRT$^\ast$, avoiding explicit collision checking of the extended paths. We prove that CBF-RRT$^\ast$ preserves the probabilistic completeness of RRT$^\ast$. Furthermore, in order to improve the sampling efficiency of the algorithm, we equip the algorithm with an adaptive sampling procedure, which is based on the cross-entropy method (CEM) for importance sampling (IS). The procedure exploits the tree of samples to focus the sampling in promising regions of the configuration space. We demonstrate the efficacy of the proposed algorithms through simulation examples., Comment: Submitted to CDC2022

Control Barrier Functions (CBFs) are becoming popular tools in guaranteeing safety for nonlinear systems and constraints, and they can reduce a constrained optimal control problem into a sequence of Quadratic Programs (QPs) for affine control systems. The recently proposed High Order Control Barrier Functions (HOCBFs) work for arbitrary relative degree constraints. One of the challenges in a HOCBF is to address the relative degree problem when a system has multiple control inputs, i.e., the relative degree could be defined with respect to different components of the control vector. This paper proposes two methods for HOCBFs to deal with systems with multiple control inputs: a general integral control method and a method which is simpler but limited to specific classes of physical systems. When control bounds are involved, the feasibility of the above mentioned QPs can also be significantly improved with the proposed methods. We illustrate our approaches on a unicyle model with two control inputs, and compare the two proposed methods to demonstrate their effectiveness and performance., Comment: To appear in ACC2022

We present a computational framework for synthesis of distributed control strategies for a heterogeneous team of robots in a partially observable environment. The goal is to cooperatively satisfy specifications given as Truncated Linear Temporal Logic (TLTL) formulas. Our approach formulates the synthesis problem as a stochastic game and employs a policy graph method to find a control strategy with memory for each agent. We construct the stochastic game on the product between the team transition system and a finite state automaton (FSA) that tracks the satisfaction of the TLTL formula. We use the quantitative semantics of TLTL as the reward of the game, and further reshape it using the FSA to guide and accelerate the learning process. Simulation results demonstrate the efficacy of the proposed solution under demanding task specifications and the effectiveness of reward shaping in significantly accelerating the speed of learning., Comment: 12 pages, 4 figures, accepted by L4DC 2022

This paper studies the problem of utilizing data-driven adaptive control techniques to guarantee stability and safety of uncertain nonlinear systems with high relative degree. We first introduce the notion of a High Order Robust Adaptive Control Barrier Function (HO-RaCBF) as a means to compute control policies guaranteeing satisfaction of high relative degree safety constraints in the face of parametric model uncertainty. The developed approach guarantees safety by initially accounting for all possible parameter realizations but adaptively reduces uncertainty in the parameter estimates leveraging data recorded online. We then introduce the notion of an Exponentially Stabilizing Adaptive Control Lyapunov Function (ES-aCLF) that leverages the same data as the HO-RaCBF controller to guarantee exponential convergence of the system trajectory. The developed HO-RaCBF and ES-aCLF are unified in a quadratic programming framework, whose efficacy is showcased via two numerical examples that, to our knowledge, cannot be addressed by existing adaptive control barrier function techniques., Comment: Accepted to the 2022 American Control Conference

Model-free continuous control for robot navigation tasks using Deep Reinforcement Learning (DRL) that relies on noisy policies for exploration is sensitive to the density of rewards. In practice, robots are usually deployed in cluttered environments, containing many obstacles and narrow passageways. Designing dense effective rewards is challenging, resulting in exploration issues during training. Such a problem becomes even more serious when tasks are described using temporal logic specifications. This work presents a deep policy gradient algorithm for controlling a robot with unknown dynamics operating in a cluttered environment when the task is specified as a Linear Temporal Logic (LTL) formula. To overcome the environmental challenge of exploration during training, we propose a novel path planning-guided reward scheme by integrating sampling-based methods to effectively complete goal-reaching missions. To facilitate LTL satisfaction, our approach decomposes the LTL mission into sub-goal-reaching tasks that are solved in a distributed manner. Our framework is shown to significantly improve performance (effectiveness, efficiency) and exploration of robots tasked with complex missions in large-scale cluttered environments. A video demonstration can be found on YouTube Channel: https://youtu.be/yMh_NUNWxho., Comment: IEEE Robotics and Automation Letters

Real-time and human-interpretable decision-making in cyber-physical systems is a significant but challenging task, which usually requires predictions of possible future events from limited data. In this paper, we introduce a time-incremental learning framework: given a dataset of labeled signal traces with a common time horizon, we propose a method to predict the label of a signal that is received incrementally over time, referred to as prefix signal. Prefix signals are the signals that are being observed as they are generated, and their time length is shorter than the common horizon of signals. We present a novel decision-tree based approach to generate a finite number of Signal Temporal Logic (STL) specifications from the given dataset, and construct a predictor based on them. Each STL specification, as a binary classifier of time-series data, captures the temporal properties of the dataset over time. The predictor is constructed by assigning time-variant weights to the STL formulas. The weights are learned by using neural networks, with the goal of minimizing the misclassification rate for the prefix signals defined over the given dataset. The learned predictor is used to predict the label of a prefix signal, by computing the weighted sum of the robustness of the prefix signal with respect to each STL formula. The effectiveness and classification performance of our algorithm are evaluated on an urban-driving and a naval-surveillance case studies.

Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal logic specifications from data. We introduce SVM-STL, an extension of Signal Signal Temporal Logic (STL), capable of specifying spatial and temporal properties of a wide range of dynamical systems that exhibit time-varying spatial patterns. Our framework utilizes machine learning techniques to learn SVM-STL specifications from system executions given by sequences of spatial patterns. We present methods to deal with both labeled and unlabeled data. In addition, given system requirements in the form of SVM-STL specifications, we provide an approach for parameter synthesis to find parameters that maximize the satisfaction of such specifications. Our learning framework and parameter synthesis approach are showcased in an example of a reaction-diffusion system., Comment: 12 pages, submitted to L4DC 2021

Time-series data classification is central to the analysis and control of autonomous systems, such as robots and self-driving cars. Temporal logic-based learning algorithms have been proposed recently as classifiers of such data. However, current frameworks are either inaccurate for real-world applications, such as autonomous driving, or they generate long and complicated formulae that lack interpretability. To address these limitations, we introduce a novel learning method, called Boosted Concise Decision Trees (BCDTs), to generate binary classifiers that are represented as Signal Temporal Logic (STL) formulae. Our algorithm leverages an ensemble of Concise Decision Trees (CDTs) to improve the classification performance, where each CDT is a decision tree that is empowered by a set of techniques to generate simpler formulae and improve interpretability. The effectiveness and classification performance of our algorithm are evaluated on naval surveillance and urban-driving case studies., Comment: arXiv admin note: text overlap with arXiv:2105.11508

Autonomous vehicles must balance a complex set of objectives. There is no consensus on how they should do so, nor on a model for specifying a desired driving behavior. We created a dataset to help address some of these questions in a limited operating domain. The data consists of 92 traffic scenarios, with multiple ways of traversing each scenario. Multiple annotators expressed their preference between pairs of scenario traversals. We used the data to compare an instance of a rulebook, carefully hand-crafted independently of the dataset, with several interpretable machine learning models such as Bayesian networks, decision trees, and logistic regression trained on the dataset. To compare driving behavior, these models use scores indicating by how much different scenario traversals violate each of 14 driving rules. The rules are interpretable and designed by subject-matter experts. First, we found that these rules were enough for these models to achieve a high classification accuracy on the dataset. Second, we found that the rulebook provides high interpretability without excessively sacrificing performance. Third, the data pointed to possible improvements in the rulebook and the rules, and to potential new rules. Fourth, we explored the interpretability vs performance trade-off by also training non-interpretable models such as a random forest. Finally, we make the dataset publicly available to encourage a discussion from the wider community on behavior specification for AVs. Please find it at github.com/bassam-motional/Reasonable-Crowd., Comment: Accepted to IROS 2021 8 pages, 7 figures, 2 tables

We develop optimal control strategies for autonomous vehicles (AVs) that are required to meet complex specifications imposed as rules of the road (ROTR) and locally specific cultural expectations of reasonable driving behavior. We formulate these specifications as rules, and specify their priorities by constructing a priority structure, called \underline{T}otal \underline{OR}der over e\underline{Q}uivalence classes (TORQ). We propose a recursive framework, in which the satisfaction of the rules in the priority structure are iteratively relaxed in reverse order of priority. Central to this framework is an optimal control problem, where convergence to desired states is achieved using Control Lyapunov Functions (CLFs) and clearance with other road users is enforced through Control Barrier Functions (CBFs). We present offline and online approaches to this problem. In the latter, the AV has limited sensing range that affects the activation of the rules, and the control is generated using a receding horizon (Model Predictive Control, MPC) approach. We also show how the offline method can be used for after-the-fact (offline) pass/fail evaluation of trajectories - a given trajectory is rejected if we can find a controller producing a trajectory that leads to less violation of the rule priority structure. We present case studies with multiple driving scenarios to demonstrate the effectiveness of the algorithms, and to compare the offline and online versions of our proposed framework., Comment: under review in TAC, 16 pages. arXiv admin note: substantial text overlap with arXiv:2101.05709