Research

In this work, we propose a Stochastic MPC (SMPC) formulation for autonomous driving at traffic intersections which incorporates multi-modal GMM predictions of surrounding vehicles for collision avoidance constraints. Our main theoretical contribution is an SMPC formulation that optimizes over a novel feedback policy class designed to exploit additional structure in the GMM predictions, and that is amenable to convex programming. We evaluate our algorithm along axes of mobility, comfort, conservatism, and computational efficiency at a simulated intersection in CARLA. To demonstrate the impact of optimizing over feedback policies, we compare our algorithm with two SMPC baselines that handle multi-modal collision avoidance chance constraints by optimizing over open-loop sequences.

• Nair*, S.H., Govindarajan*, V., Lin, T., Meissen, C., Tseng, E.H., Borrelli, F. "Stochastic MPC with Multi-modal Predictions for Traffic Intersections", submitted to ICRA 2022 (https://arxiv.org/abs/2109.09792)

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodelled dynamics, and (ii) computation of positive invariant sets.

• Nair, S.H., Bujarbaruah, M. , Borrelli, F. "Modeling of Dynamical Systems via Successive Graph Approximations", 21st IFAC World Congress 2020 (IFAC 2020) (https://arxiv.org/abs/1910.03719)

In this work, we propose an Adaptive MPC framework for linear systems with additive state-dependent uncertainty. The additive (possibly nonlinear) state-dependent uncertainty is modeled and learned using the technique of successive graph approximations based on our IFAC 2020 paper. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction of state and input constraints for the closed loop system for all realisations of the system model.

• Bujarbaruah*, M. , Nair*, S.H., Borrelli, F. "A Semi-Definite Programming Approach to Robust Adaptive MPC under State Dependent Uncertainty", 18th European Control Conference 2020 (ECC 2020) (https://arxiv.org/abs/1910.04378)

*denotes equal contribution

In this work, we propose a Learning Model Predictive Control (LMPC) for difference flat systems performing iterative tasks. This article builds on previous work on LMPC and improves its computational tractability for the class of systems under consideration. We show how to construct a convex safe set in a lifted space of specific outputs called flat outputs and its associated convex value function approximation. The convex safe set and convex value function are updated using historical data and those are used to iteratively synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability and non-decreasing closed-loop performance at each policy update.

• Nair, S.H., Rosolia, U., Borrelli, F. "Output-Lifted Learning Model Predictive Control for Flat Systems" (https://arxiv.org/abs/2004.05173)

The video demonstrates the Learning Model Predictive Strategy from the article "Learning How to Autonomously Race a Car: A Predictive Control Approach", IEEE Transactions on Control Systems Technology implemented on the Hyundai Genesis at Hyundai's California Proving Grounds. The minimum time optimal control problem for racing along the track is tackled using the LMPC strategy. Using a subset of the stored data, an approximation of value function is constructed and updated iteratively. For system identification, a structured Affine Time Varying (ATV) model is constructed using kernel-based local linear regression on a subset of the stored data and knowledge of the vehicle's kinematics.

In this work, we develop variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and subsequently solved to obtain necessary conditions that characterise optimal trajectories.

This work was done under the guidance of Prof. Ravi N. Banavar for my Master's thesis. More details can be found here:

• Nair, S.H., Banavar, R.N., "Discrete Optimal Control of Interconnected Mechanical Systems", 11th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2019) (https://arxiv.org/abs/1809.09191)

In this work, we consider a spacecraft formation problem wherein there are asymmetric, bounded and time-varying delays in the communication links between the spacecraft while the feedback from the spacecraft’s own states is instantaneous.

This work was done under the guidance of Prof. Kamesh Subbarao during my internship at The University of Texas at Arlington in the summer of 2016. More details can be found here:

• Nair, S.H., Subbarao, K., "Attitude Control of Spacecraft Formations subject to Distributed Communication Delays", 27th AAS/AIAA Space Flight Mechanics Meeting 2017 (https://arxiv.org/abs/1707.01185)

Space-filling curves are primarily used in applications that require visiting various regions in a space. In this work, we address tracing the Hilbert's space-filling curve in regions with obstacles.

This work was done under the guidance of Prof. Arpita Sinha and Prof. Leena Vachhani, and also won the Undergraduate Research Award-01. More details can be found here:

• Nair, S.H., Sinha, A., Vachhani, L., "Hilbert’s Space-filling Curve for Regions with Holes", 56th IEEE Conference on Decision and Control, 2017 (https://arxiv.org/abs/1709.02938)

In this work, we designed a class of control laws to achieve circumnavigation in a GPS-denied environment using range and range-rate information. Unlike earlier works, the control laws presented are non-switching and continuous. Owing to the bounded nature of the control law, a limit on the gain is derived to account for turn rate limitations. This work was done under the guidance of Prof. Ashwini Ratnoo during my internship at the Indian Institute of Science, Bangalore in the summer of 2015.

• Nair, S.H., Ratnoo, A., "A class of control laws for circumnavigation in GPS-denied areas using range and range-rate information" (Project Report)