Sriram Sankaranarayanan

selected publications

1. Template-Based Piecewise Affine Regression

   Guillaume O. Berger, and Sriram Sankaranarayanan

   Research Directions: Cyber-Physical Systems, TBA (TBA) pp. TBA, 2024.

   Note: In Press: Extended version of our L4DC Paper..

   Abs Bib URL

   We study the problem of fitting a piecewise affine (PWA) function to input–output data. Our algorithm divides the input domain into finitely many regions whose shapes are specified by a user-provided template and such that the input-output data in each region are fit by an affine function within a user-provided error tolerance. We first prove that this problem is NP-hard. Then, we present a top-down algorithmic approach for solving the problem. The algorithm considers subsets of the data points in a systematic manner, trying to fit an affine function for each subset using linear regression. If regression fails on a subset, the algorithm extracts a minimal set of points from the subset (an unsatisfiable core) that is responsible for the failure. The identified core is then used to split the current subset into smaller ones. By combining this top-down scheme with a set-covering algorithm, we derive an overall approach that provides optimal PWA models for a given error tolerance, where optimality refers to minimizing the number of pieces of the PWA model. We demonstrate our approach on three numerical examples that include PWA approximations of a widely used nonlinear insulin-glucose regulation model and a double inverted pendulum with soft contacts.

           @article{ Berger+Sankaranarayanan/2024/Template,
           title = { Template-Based Piecewise Affine Regression },
           author = {   Berger, Guillaume O.  and    Sankaranarayanan, Sriram   },
           journal = { Research Directions: Cyber-Physical Systems },  
           year = { 2024 },  
           publisher = { Cambridge University Press }, 
           pages = { TBA }, 
           
           
           volume = { TBA },  
           number = { TBA },  
           
           }
           

2. Anticipating Oblivious Opponents in Stochastic Games

   Shadi Tasdighi Kalat, Sriram Sankaranarayanan, and Ashutosh Trivedi

   In Workshop on Algorithmic Foundations of Robotics (WAFR), pp. TBA, 2024.

   Note: To Appear.

   Abs Bib URL

   We present an approach for systematically anticipating the actions and policies employed by oblivious environments in concurrent stochastic games, while maximizing a reward function. Our main contribution lies in the synthesis of a finite information state machine (ISM) whose alphabet ranges over the actions of the environment. Each state of the ISM is mapped to a belief state about the policy used by the environment. We introduce a notion of consistency that guarantees that the belief states tracked by the ISM stays within a fixed distance of the precise belief state obtained by knowledge of the full history. We provide methods for checking consistency of an automaton and a synthesis approach which, upon successful termination, yields an ISM. We construct a Markov Decision Process (MDP) that serves as the starting point for computing optimal policies for maximizing a reward function defined over plays. We present an experimental evaluation over benchmark examples including human activity data for tasks such as cataract surgery and furniture assembly, wherein our approach successfully anticipates the policies and actions of the environment in order to maximize the reward.

           @inproceedings{ Kalat+Others/2024/Anticipating,
           title = { Anticipating Oblivious Opponents in Stochastic Games },
           author = {   Kalat, Shadi Tasdighi  and    Sankaranarayanan, Sriram  and    Trivedi, Ashutosh   },
           booktitle= { Workshop on Algorithmic Foundations of Robotics (WAFR) },  
           year = { 2024 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

3. Automated Assessment and Adaptive Multimodal Formative Feedback Improves Psychomotor Skills Training Outcomes in Quadrotor Teleoperation

   Emily Jensen, Sriram Sankaranarayanan, and Bradley Hayes

   In Proceedings of Human Agent Interaction (HAI), pp. TBA, 2024.

   Note: To Appear.

   Abs Bib URL

   The workforce will need to continually upskill in order to meet the evolving demands of industry, especially working with robotic and autonomous systems. Current training methods are not scalable and do not adapt to the skills that learners already possess. In this work, we develop a system that automatically assesses learner skill in a quadrotor teleoperation task using temporal logic task specifications. This assessment is used to generate multimodal feedback based on the principles of effective formative feedback. Participants perceived the feedback positively. Those receiving formative feedback viewed the feedback as more actionable compared to receiving summary statistics. Participants in the multimodal feedback condition were more likely to achieve a safe landing and increased their safe landings more over the experiment compared to other feedback conditions. Finally, we identify themes to improve adaptive feedback and discuss and how training for complex psychomotor tasks can be integrated with learning theories.

           @inproceedings{ Jensen+Others/2024/Automated,
           title = { Automated Assessment and Adaptive Multimodal Formative Feedback Improves Psychomotor Skills Training Outcomes in Quadrotor
   Teleoperation },
           author = {   Jensen, Emily  and    Sankaranarayanan, Sriram  and    Hayes, Bradley   },
           booktitle= { Proceedings of Human Agent Interaction (HAI) },  
           year = { 2024 },  
           
           pages = { TBA }, 
           
           
           
           
           
           }
           

4. Cone-Based Abstract Interpretation for Nonlinear Positive Invariant Synthesis

   Guillaume O. Berger, Masoumeh Ghanbarpour, and Sriram Sankaranarayanan

   In Hybrid Systems: Computation and Control (HSCC), pp. 12:1-12:16, 2024.

   Abs Bib URL

   We present an abstract interpretation approach for synthesizing nonlinear (semi-algebraic) positive invariants for systems of polynomial ordinary differential equations (ODEs) and switched systems. The key behind our approach is to connect the system under study to a positive nonlinear system through a “change of variables”. The positive invariance of the first orthant (R+) for a positive system guarantees, in turn, that the functions involved in the change of variables define a positive invariant for the original system. The challenge lies in discovering such functions for a given system. To this end, we characterize positive invariants as fixed points under an operator that is defined using the Lie derivative. Next, we use abstract-interpretation approaches to systematically compute this fixed point. Whereas abstract interpretation has been applied to the static analysis of programs, and invariant synthesis for hybrid systems to a limited extent, we show how these approaches can compute fixed points over cones generated by polynomials using sum-of-squares optimization and its relaxations. Our approach is shown to be promising over a set of small but hard-to-analyze nonlinear models, wherein it is able to generate positive invariants to place useful bounds on their reachable sets.

           @inproceedings{ Berger+Ghanbarpour+Sankaranarayanan/2024/Cone,
           title = { Cone-Based Abstract Interpretation for Nonlinear Positive Invariant Synthesis },
           author = {   Berger, Guillaume O.  and    Ghanbarpour, Masoumeh  and    Sankaranarayanan, Sriram   },
           booktitle= { Hybrid Systems: Computation and Control (HSCC) },  
           year = { 2024 },  
           publisher = { ACM }, 
           pages = { 12:1-12:16 }, 
           
           
           
           
           
           }