[C68] An Optimal Control Framework for Influencing Human Driving Behavior in Mixed-Autonomy Traffic
Anirudh Chari, Rui Chen, Jaskaran Grover and Changliu Liu
American Control Conference, 2024
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2023
[T1] System Identification and Control of Multiagent Systems Through Interactions
Jaskaran Singh Grover
PhD Thesis, 2023
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Abstract:
This thesis investigates the problem of inferring the underlying dynamic model of individual agents of a multiagent system (MAS) and using these models to shape the MAS’s behavior using robots extrinsic to the MAS. We investigate (a) how an observer can infer the latent task and inter-agent interaction constraints from the agents’ motion and (b) how the observer can elicit a desired behavior out of the MAS by orchestrating its interactions with robots. The ability to learn individual dynamics models of an aggregated system has several applications such as learning local rules in biological swarms that give rise to emergent behavior and learning tactics of an adversarial multirobot team. Likewise, the ability to shape behavior using extrinsic robots can be used to defend against an adversarial team of robots and guide humans using robots as in social navigation.
The first part of this thesis focuses on the model learning problem. We model agents as integrators that solve a reactive optimization to calculate velocities for mediating between goal-directed motions and collision avoidance with other agents. We develop several estimators that allow an observer to infer this model’s parameters and show that the learned parameters indeed rationalize the observed motions. Necessary identifiability conditions are derived that guarantee correct inference. Our proposed estimators include adaptive observers, Kalman filters and several inverse optimization algorithms that are robust to both measurement noise and model mismatch. To demonstrate this robustness, we evaluate these estimators on a pedestrian dataset and learn each pedestrian’s desired velocity, aggressiveness coefficients and safety margins with walls, obstacles and other pedestrians.
The second part of this thesis focuses on eliciting a desired behavior out of the MAS by inducing interactions with robots. While the theory we develop is general, we consider the dog-sheep herding problem as a use case that requires controlling dog robots to repel sheep agents from a critical zone. We incorporate non-collocated feedback linearization in an optimization-based framework to compute the desired controls for the dogs. Both centralized and distributed implementations are developed to cater to the scalability, feasibility and budget-efficiency objectives. We validate the correctness of these controllers in multiple experiments on the CMU multirobot arena. We also develop a robust extension of these controllers, which we term control-barrier function based semidefinite programs (CBF-SDPs), that guarantee zone defense despite uncertainty in the sheep’s dynamics. Finally, we conclude this thesis with an integration of the robust model learning algorithms with robust control algorithms followed by experimental validation on the multirobot arena.
2022
[J11] The before, during, and after of multi-robot deadlock
Jaskaran Grover, Changliu Liu and Katia Sycara
The International Journal of Robotics Research, 2022
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Collision avoidance for multirobot systems is a well-studied problem. Recently, control barrier functions (CBFs) have been proposed for synthesizing controllers that guarantee collision avoidance and goal stabilization for multiple robots. However, it has been noted that reactive control synthesis methods (such as CBFs) are prone to deadlock, an equilibrium of system dynamics that causes the robots to stall before reaching their goals. In this paper, we analyze the closed-loop dynamics of robots using CBFs, to characterize controller parameters, initial conditions, and goal locations that invariably lead the system to deadlock. Using tools from duality theory, we derive geometric properties of robot configurations of an N robot system once it is in deadlock and we justify them using the mechanics interpretation of KKT conditions. Our key deductions are that 1) system deadlock is characterized by a force-equilibrium on robots and 2) deadlock occurs to ensure safety when safety is on the brink of being violated. These deductions allow us to interpret deadlock as a subset of the state space, and we show that this set is non-empty and located on the boundary of the safe set. By exploiting these properties, we analyze the number of admissible robot configurations in deadlock and develop a provably-correct decentralized algorithm for deadlock resolution to safely deliver the robots to their goals. This algorithm is validated in simulations as well as experimentally on Khepera-IV robots.
[C51] Distributed multirobot control for non-cooperative herding
Nishant Mohanty, Jaskaran Grover, Changliu Liu and Katia Sycara
International Symposium on Distributed Autonomous Robotic Systems, 2022
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In this paper, we consider the problem of protecting a high-value area from being breached by sheep agents by crafting motions for dog robots. We use control barrier functions to pose constraints on the dogs’ velocities that induce repulsion in the sheep relative to the high-value area. This paper extends the results developed in our prior work on the same topic in three ways. Firstly, we implement and validate our previously developed centralized herding algorithm on many robots. We show herding of up to five sheep agents using three dog robots. Secondly, as an extension to the centralized approach, we develop two distributed herding algorithms, one favoring feasibility while the other favoring optimality. In the first algorithm, we allocate a unique sheep to a unique dog, making that dog responsible for herding its allocated sheep away from the protected zone. We provide feasibility proof for this approach, along with numerical simulations. In the second algorithm, we develop an iterative distributed reformulation of the centralized algorithm, which inherits the optimality (i.e. budget efficiency) from the centralized approach. Lastly, we conduct real-world experiments of these distributed algorithms and demonstrate herding of up to five sheep agents using five dog robots.
[C49] Semantically-Aware Pedestrian Intent Prediction With Barrier Functions and Mixed-Integer Quadratic Programming
Jaskaran Grover, Yiwei Lyu, Wenhao Luo, Changliu Liu, John Dolan and Katia Sycara
IFAC Workshop on Cyber-Physical Human Systems, 2022 Best Student Paper Finalist
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[C48] Noncooperative Herding With Control Barrier Functions: Theory and Experiments
Jaskaran Grover, Nishant Mohanty, Wenhao Luo, Changliu Liu and Katia Sycara
IEEE Conference on Decision and Control, 2022
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[U] Control barrier functions-based semi-definite programs (cbf-sdps): Robust safe control for dynamic systems with relative degree two safety indices
Jaskaran Singh Grover, Changliu Liu and Katia Sycara
arXiv:2208.12252, 2022
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2021
[C39] Parameter Identification for Multirobot Systems Using Optimization-based Controllers
Jaskaran Grover, Changliu Liu and Katia Sycara
2021 International Symposium on Multi-Robot and Multi-Agent Systems (MRS), 2021
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This paper considers the problem of parameter identification for a multirobot system. We wish to understand when is it feasible for an adversarial observer to reverse-engineer the parameters of tasks being performed by a team of robots by simply observing their positions. We address this question by using the concept of persistency of excitation from system identification. Each robot in the team uses optimization-based controllers for mediating between task satisfaction and collision avoidance. These controllers exhibit an implicit dependence on the task’s parameters which poses a hurdle for deriving necessary conditions for parameter identification, since such conditions usually require an explicit relation. We address this bottleneck by using duality theory and SVD of active collision avoidance constraints and derive an explicit relation between each robot’s task parameters and its control inputs. This allows us to derive the main necessary conditions for successful identification which agree with our intuition. We demonstrate the importance of these conditions through numerical simulations by using (a) an adaptive observer and (b) an unscented Kalman filter for goal estimation in various geometric settings. These simulations show that under circumstances where parameter inference is supposed to be infeasible per our conditions, both these estimators fail and likewise when it is feasible, both converge to the true parameters.
[C36] System Identification for Safe Controllers using Inverse Optimization
Jaskaran Singh Grover, Changliu Liu and Katia Sycara
Modeling, Estimation, and Control Conference, 2021
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This paper presents algorithms for learning parameters of optimization-based controllers used in multiagent systems based on their position-velocity measurements. The motivation to learn these parameters stems from the need to infer an agent’s intent (human or robot) to facilitate accurate predictions of motion as well as efficient interactions in a multiagent system. In this work, we demonstrate how to perform inference using algorithms based on the theory of inverse optimization (IO). We propose QP-based reformulations of IO algorithms for faster processing of batch-data to facilitate quicker inference. In our prior work, we used persistency of excitation analysis for deriving conditions under which conventional estimators such as a Kalman filter can successfully perform such inference. In this work, we demonstrate that whenever these conditions are violated, inference of parameters will fail, be it using IO-based algorithms or a UKF. We provide numerical simulations to infer desired goal locations and controller gains of each robot in a multirobot system and compare performance of IO-based algorithms with a UKF and an adaptive observer. In addition to these, we also conduct experiments with Khepera-4 robots and demonstrate the power of IO-based algorithms in inferring goals in the presence of perception noise.
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[C34] Feasible Region-based Identification Using Duality
Jaskaran Grover, Changliu Liu and Katia Sycara
European Control Conference, 2021
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We consider the problem of estimating bounds on parameters representing tasks being performed by individual robots in a multirobot system. In our previous work, we derived necessary conditions based on persistency of excitation analysis for exact identification of these parameters. We concluded that depending on the robot’s task, the dynamics of individual robots may fail to satisfy these conditions, thereby preventing exact inference. As an extension to that work, this paper focuses on estimating bounds on task parameters when such conditions are not satisfied. Each robot in the team uses optimization-based controllers for mediating between task satisfaction and collision avoidance. We use KKT conditions of this optimization and SVD of active collision avoidance constraints to derive explicit relations between Lagrange multipliers, robot dynamics and task parameters. Using these relations, we are able to derive bounds on each robot’s task parameters. Through numerical simulations we show how our proposed region based identification approach generates feasible regions for parameters when a conventional estimator such as a UKF fails. Additionally, empirical evidence shows that this approach generates contracting sets which converge to the true parameters much faster than the rate at which a UKF based estimate converges. Videos of these results are available at https://bit.ly/2JDMgeJ.
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[W] Simultaneously learning safety margins and task parameters of multirobot systems
Jaskaran Singh Grover, Changliu Liu and Katia Sycara
RSS BI-MAS Workshop, 2021
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We present an algorithm for learning constraint and objective function parameters of optimization-based controllers used in multirobot systems. Our proposed approach uses position-velocity measurements of each robot in the team to perform this inference. The motivation to learn these parameters stems from the need to infer an agent’s intent for accurate predictions of motion in a multiagent system. We develop an extension of our prior work in which we performed task learning assuming constraint parameters were known. In this work, we perform simultaneous learning of constraint and cost function parameters by posing it as a constrained nonconvex optimization problem. The cost function parameters that we learn encode information of the task being performed by each robot in the team whereas the constraint parameters encode information about individual safety margin distances and size of the safe control set for each robot. Our simulation results show the accurate reconstruction of both the constraint and cost function parameters and we analyze some failure cases.
2020
[C28] Deadlock Analysis and Resolution in Multi-Robot Systems
Jaskaran Grover, Changliu Liu and Katia Sycara
International Workshop on the Algorithmic Foundations of Robotics, 2020
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Collision avoidance for multirobot systems is a well studied problem. Recently, control barrier functions (CBFs) have been proposed for synthesizing controllers guarantee collision avoidance and goal stabilization for multiple robots. However, it has been noted reactive control synthesis methods (such as CBFs) are prone to deadlock, an equilibrium of system dynamics causes robots to come to a standstill before reaching their goals. In this paper, we formally derive characteristics of deadlock in a multirobot system uses CBFs. We propose a novel approach to analyze deadlocks resulting from optimization based controllers (CBFs) by bor- rowing tools from duality theory and graph enumeration. Our key insight is system deadlock is characterized by a force-equilibrium on robots and we show how complexity of deadlock analysis increases approximately exponentially with the number of robots. This analysis allows us to interpret deadlock as a subset of the state space, and we prove this set is non-empty, bounded and located on the boundary of the safety set. Finally, we use these properties to develop a provably correct decentralized algorithm for deadlock resolution which ensures robots converge to their goals while avoiding collisions. We show simulation results of the resolution algorithm for two and three robots and experimentally validate this algorithm on Khepera-IV robots.
[C25] Why Does Symmetry Cause Deadlocks?
Jaskaran Grover, Changliu Liu and Katia Sycara
IFAC-PapersOnLine, 2020
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Collision avoidance for multirobot systems has been studied thoroughly. Recently, control barrier functions (CBFs) have been proposed to mediate between collision avoidance and goal achievement for multiple robots. However, it has been noted that reactive controllers (such as CBFs) are prone to deadlock, an equilibrium that causes the robots to stall before reaching their goals. In this paper, we formally analyze two and three robot systems and discover circumstances under which CBFs cause deadlocks using duality theory. For the two robot system, we consider mutually heterogeneous robots (such as one more vigorous or closer to its goal than the other) and prove that this heterogeneity does not help in preventing deadlock. We then consider three robots, and conclude from these two scenarios that the geometric symmetry resulting from robots’ initial positions and goals constrains CBFs to generate velocities that render deadlock stable. Thus, conferring skewness to the system can help evade deadlock.
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[W] “Provably Safe” in the Wild: Testing Control Barrier Functions on a Vision-Based Quadrotor in an Outdoor Environment
Cherie Ho, Katherine Shih, Jaskaran Singh Grover, Changliu Liu and Sebastian Scherer
Proceedings of RSS ’20 2nd Workshop on Robust Autonomy: Safe Robot Learning and Control in Uncertain Real-World Environments, 2020
