arXiv subjects

Pushpak Jagtap

Publications and source records attributed to Pushpak Jagtap.

At least 73 records · Page 4Linked to original sources

arXiv2024

Real Time Safety of Fixed-wing UAVs using Collision Cone Control Barrier Functions

Fixed-wing UAVs have transformed the transportation system with their high flight speed and long endurance, yet their safe operation in increasingly cluttered environments depends heavily on effective collision avoidance techniques. This paper presents a novel method for safely navigating an aircraft along a desired route while avoiding moving obstacles. We utilize a class of control barrier functions (CBFs) based on collision cones to ensure the relative velocity between the aircraft and the obstacle consistently avoids a cone of vectors that might lead to a collision. By demonstrating that the proposed constraint is a valid CBF for the aircraft, we can leverage its real-time implementation via Quadratic Programs (QPs), termed the CBF-QPs. Validation includes simulating control law along trajectories, showing effectiveness in both static and moving obstacle scenarios.

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arXiv2024

Temporal Logic Resilience for Dynamical Systems

We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the acceptable functionality and define the resilience metric as the maximum disturbance under which the system satisfies the temporal requirements. We fix a parameterized template for the set of disturbances and form a robust optimization problem under the system dynamics and the temporal specifications to find the maximum value of the parameter. Additionally, we introduce two novel classes of specifications: closed and convex finite temporal logics specifications, offering a comprehensive analysis of the resilience metric within these specific frameworks. From a computational standpoint, we present an exact solution for linear systems and exact-time reachability and finite-horizon safety, complemented by an approximate solution for finite-horizon reachability. Extending our findings to nonlinear systems, we leverage linear approximations and SMT-based approaches to offer viable computational methodologies. The theoretical results are demonstrated on the temperature regulation of buildings, adaptive cruise control and DC motors.

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arXiv2024

Barrier Functions Inspired Reward Shaping for Reinforcement Learning

Reinforcement Learning (RL) has progressed from simple control tasks to complex real-world challenges with large state spaces. While RL excels in these tasks, training time remains a limitation. Reward shaping is a popular solution, but existing methods often rely on value functions, which face scalability issues. This paper presents a novel safety-oriented reward-shaping framework inspired by barrier functions, offering simplicity and ease of implementation across various environments and tasks. To evaluate the effectiveness of the proposed reward formulations, we conduct simulation experiments on CartPole, Ant, and Humanoid environments, along with real-world deployment on the Unitree Go1 quadruped robot. Our results demonstrate that our method leads to 1.4-2.8 times faster convergence and as low as 50-60% actuation effort compared to the vanilla reward. In a sim-to-real experiment with the Go1 robot, we demonstrated better control and dynamics of the bot with our reward framework.

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arXiv2024

Learning a Formally Verified Control Barrier Function in Stochastic Environment

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee and performance of safe controllers rely on the construction of valid CBFs. Inspired by universal approximatability, CBFs are represented by neural networks, known as neural CBFs (NCBFs). This paper presents an algorithm for synthesizing formally verified continuous-time neural Control Barrier Functions in stochastic environments in a single step. The proposed training process ensures efficacy across the entire state space with only a finite number of data points by constructing a sample-based learning framework for Stochastic Neural CBFs (SNCBFs). Our methodology eliminates the need for post hoc verification by enforcing Lipschitz bounds on the neural network, its Jacobian, and Hessian terms. We demonstrate the effectiveness of our approach through case studies on the inverted pendulum system and obstacle avoidance in autonomous driving, showcasing larger safe regions compared to baseline methods.

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arXiv2024

A Collision Cone Approach for Control Barrier Functions

This work presents a unified approach for collision avoidance using Collision-Cone Control Barrier Functions (CBFs) in both ground (UGV) and aerial (UAV) unmanned vehicles. We propose a novel CBF formulation inspired by collision cones, to ensure safety by constraining the relative velocity between the vehicle and the obstacle to always point away from each other. The efficacy of this approach is demonstrated through simulations and hardware implementations on the TurtleBot, Stoch-Jeep, and Crazyflie 2.1 quadrotor robot, showcasing its effectiveness in avoiding collisions with dynamic obstacles in both ground and aerial settings. The real-time controller is developed using CBF Quadratic Programs (CBF-QPs). Comparative analysis with the state-of-the-art CBFs highlights the less conservative nature of the proposed approach. Overall, this research contributes to a novel control formation that can give a guarantee for collision avoidance in unmanned vehicles by modifying the control inputs from existing path-planning controllers.

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arXiv2023

Symbolic Models for Interconnected Impulsive Systems

In this paper, we present a compositional methodology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of "alternating simulation function" to establish a relationship between concrete subsystems and their symbolic models. Assuming some small-gain type conditions, we develop an alternating simulation function between the symbolic models of individual subsystems and those of the nonlinear interconnected impulsive systems. To construct symbolic models of nonlinear impulsive subsystems, we propose an approach that depends on incremental input-to-state stability and forward completeness properties. Finally, we demonstrate the advantages of our framework through a case study.

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arXiv2023

Barrier Function-based Distributed Symbolic Controller for Multi-Agent Systems

Because of the scalability issues associated with the symbolic controller synthesis approach, employing it in a multi-agent system (MAS) framework becomes difficult. In this paper, we present a novel approach for synthesizing distributed symbolic controllers for MAS, that enforces a local Linear Temporal Logic (LTL) specification on each agent and global safety specifications on the MAS, in a computationally efficient manner by leveraging the concept of control barrier functions (CBF). In addition, we also provide an analysis on the effect of the CBF parameters on the conservatism introduced by our proposed approach in the size and domain of the synthesized controller. The effectiveness of this approach is demonstrated through a comparison with the conventional monolithic symbolic control, using simulation as well as hardware demonstrations.

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arXiv2023

Funnel-based Reward Shaping for Signal Temporal Logic Tasks in Reinforcement Learning

Signal Temporal Logic (STL) is a powerful framework for describing the complex temporal and logical behaviour of the dynamical system. Numerous studies have attempted to employ reinforcement learning to learn a controller that enforces STL specifications; however, they have been unable to effectively tackle the challenges of ensuring robust satisfaction in continuous state space and maintaining tractability. In this paper, leveraging the concept of funnel functions, we propose a tractable reinforcement learning algorithm to learn a time-dependent policy for robust satisfaction of STL specification in continuous state space. We demonstrate the utility of our approach on several STL tasks using different environments.

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arXiv2023

Collision Cone Control Barrier Functions: Experimental Validation on UGVs for Kinematic Obstacle Avoidance

Autonomy advances have enabled robots in diverse environments and close human interaction, necessitating controllers with formal safety guarantees. This paper introduces an experimental platform designed for the validation and demonstration of a novel class of Control Barrier Functions (CBFs) tailored for Unmanned Ground Vehicles (UGVs) to proactively prevent collisions with kinematic obstacles by integrating the concept of collision cones. While existing CBF formulations excel with static obstacles, extensions to torque/acceleration-controlled unicycle and bicycle models have seen limited success. Conventional CBF applications in nonholonomic UGV models have demonstrated control conservatism, particularly in scenarios where steering/thrust control was deemed infeasible. Drawing inspiration from collision cones in path planning, we present a pioneering CBF formulation ensuring theoretical safety guarantees for both unicycle and bicycle models. The core premise revolves around aligning the obstacle's velocity away from the vehicle, establishing a constraint to perpetually avoid vectors directed towards it. This control methodology is rigorously validated through simulations and experimental verification on the Copernicus mobile robot (Unicycle Model) and FOCAS-Car (Bicycle Model).

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arXiv2023

Funnel-based Control for Reach-Avoid-Stay Specifications

The paper addresses the problem of controller synthesis for control-affine nonlinear systems to meet reach-avoid-stay specifications. Specifically, the goal of the research is to obtain a closed-form control law ensuring that the trajectories of the nonlinear system, reach a target set while avoiding all unsafe regions and adhering to the state-space constraints. To tackle this problem, we leverage the concept of the funnel-based control approach. Given an arbitrary unsafe region, we introduce a circumvent function that guarantees the system trajectory to steer clear of that region. Subsequently, an adaptive funnel framework is proposed based on the target, followed by the construction of a closed-form controller using the established funnel function, enforcing the reach-avoid-stay specifications. To demonstrate the efficacy of the proposed funnel-based control approach, a series of simulation experiments have been carried out.

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arXiv2023

On the Efficacy and Noise-Robustness of Jointly Learned Speech Emotion and Automatic Speech Recognition

New-age conversational agent systems perform both speech emotion recognition (SER) and automatic speech recognition (ASR) using two separate and often independent approaches for real-world application in noisy environments. In this paper, we investigate a joint ASR-SER multitask learning approach in a low-resource setting and show that improvements are observed not only in SER, but also in ASR. We also investigate the robustness of such jointly trained models to the presence of background noise, babble, and music. Experimental results on the IEMOCAP dataset show that joint learning can improve ASR word error rate (WER) and SER classification accuracy by 10.7% and 2.3% respectively in clean scenarios. In noisy scenarios, results on data augmented with MUSAN show that the joint approach outperforms the independent ASR and SER approaches across many noisy conditions. Overall, the joint ASR-SER approach yielded more noise-resistant models than the independent ASR and SER approaches.

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arXiv2023

Approximation- and Chattering-free Quasi Sliding Mode Control for Unknown Systems

Motivated by the concept of Quasi-Sliding Mode (QSM) in discrete-time systems, this paper presents a novel approach that relaxes the requirement of ubiquitous exact sliding motion in continuous-time systems, aiming to achieve an approximation- and chattering-free quasi-sliding mode controller (QSMC). The proposed QSMC provides robust and chattering-free control for an unknown nonlinear system without the need for intricate control methods, learning agents, or system identification tools. Furthermore, comprehensive simulation studies have been conducted to validate the effectiveness of the proposed strategy.

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arXiv2023

Approximation-free control for unknown systems with performance and input constraints

This paper addresses the problem of tracking control for an unknown nonlinear system with time-varying bounded disturbance subjected to prescribed Performance and Input Constraints (PIC). Since simultaneous prescription of PIC involves a trade-off, we propose an analytical feasibility condition to prescribe feasible PIC which also yields feasible initial state space as corollary results. Additionally, an approximation-free controller is proposed to guarantee that the tracking performance adheres to the prescribed PIC. The effectiveness of the proposed approach is demonstrated through numerical examples.

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arXiv2022

Temporal Waypoint Navigation of Multi-UAV Payload System using Barrier Functions

Aerial package transportation often requires complex spatial and temporal specifications to be satisfied in order to ensure safe and timely delivery from one point to another. It is usually efficient to transport versatile payloads using multiple UAVs that can work collaboratively to achieve the desired task. The complex temporal specifications can be handled coherently by applying Signal Temporal Logic (STL) to dynamical systems. This paper addresses the problem of waypoint navigation of a multi-UAV payload system under temporal specifications using higher-order time-varying control barrier functions (HOCBFs). The complex nonlinear system of relative degree two is transformed into a simple linear system using input-output feedback linearization. An optimization-based control law is then derived to achieve the temporal waypoint navigation of the payload. The controller's efficacy and real-time implementability are demonstrated by simulating a package delivery scenario inside a high-fidelity Gazebo simulation environment.

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arXiv2022

Compositional Approximately Bisimilar Abstractions of Interconnected Systems

This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the symbolic model conserves the original model's dynamics. We develop a compositional approach for abstraction-based controller synthesis by relying on the notions of approximate composition and incremental input-to-state stability. In particular, given a large-scale system consisting of interconnected components, we provide conditions under which the concept of approximate (alternating) simulation relation is preserved when going from the subsystems to the large-scale interconnected system. The engineering relevance of the theoretical results has been evaluated through an application in traffic congestion control.

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arXiv2022

Approximation-free Prescribed Performance Control with Prescribed Input Constraints

This paper considers the tracking control problem for an unknown nonlinear system with time-varying bounded disturbance subjected to a prescribed performance and input constraints. When performance and input constraints are specified simultaneously for such a problem, a trade-off is inevitable. Consequently, a feasibility condition for prescribing performance and input constraints is devised to address such difficulties of arbitrary prescription. In addition, an approximation-free controller with low complexity is proposed, which ensures that the constraints are never violated, provided that the feasibility condition holds. Finally, simulation results corroborate the effectiveness of the proposed controller.

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arXiv2022

Funnel-based Reachability Control of Unknown Nonlinear Systems using Gaussian Processes

This paper aims to synthesize a reachability controller for an unknown dynamical system. We first learn the unknown system using Gaussian processes and the (probabilistic) guarantee on the learned model. Then we use the funnel-based controller synthesis approach using this approximated dynamical system to design the controller for a reachability specification. Finally, the merits of the proposed method are shown using a numerical example.

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arXiv2022

Compositional Synthesis of Signal Temporal Logic Tasks via Assume-Guarantee Contracts

In this paper, we focus on the problem of compositional synthesis of controllers enforcing signal temporal logic (STL) tasks over a class of continuous-time nonlinear interconnected systems. By leveraging the idea of funnel-based control, we show that a fragment of STL specifications can be formulated as assume-guarantee contracts. A new concept of contract satisfaction is then defined to establish our compositionality result, which allows us to guarantee the satisfaction of a global contract by the interconnected system when all subsystems satisfy their local contracts. Based on this compositional framework, we then design closed-form continuous-time feedback controllers to enforce local contracts over subsystems in a decentralized manner. Finally, we demonstrate the effectiveness of our results on two numerical examples.

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