arXiv subjects

Hassan Almubarak

Publications and source records attributed to Hassan Almubarak.

15 recordsLinked to original sources

arXiv2026

Barrier-Riccati Synthesis for Nonlinear Safe Control with Expanded Region of Attraction

We present a Riccati-based framework for safety-critical nonlinear control that integrates the barrier states (BaS) methodology with the State-Dependent Riccati Equation (SDRE) approach. The BaS formulation embeds safety constraints into the system dynamics via auxiliary states, enabling safety to be treated as a control objective. To overcome the limited region of attraction in linear BaS controllers, we extend the framework to nonlinear systems using SDRE synthesis applied to the barrier-augmented dynamics and derive a matrix inequality condition that certifies forward invariance of a large region of attraction and guarantees asymptotic safe stabilization. The resulting controller is computed online via pointwise Riccati solutions. We validate the method on an unstable constrained system and cluttered quadrotor navigation tasks, demonstrating improved constraint handling, scalability, and robustness near safety boundaries. This framework offers a principled and computationally tractable solution for synthesizing nonlinear safe feedback in safety-critical environments.

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arXiv2025

Barrier States Theory for Safety-Critical Multi-Objective Control

Multi-objective safety-critical control entails a diligent design to avoid possibly conflicting scenarios and ensure safety. This paper addresses multi-objective safety-critical control through a novel approach utilizing barrier states (BaS) to integrate safety into control design. It introduces the concept of safety embedded systems, where the safety condition is integrated with barrier functions to characterize a dynamical subsystem that is incorporated into the original model for control design. This approach reformulates the control problem to focus on designing a control law for an unconstrained system, ensuring that the barrier state remains bounded while achieving other performance objectives. The paper demonstrates that designing a stabilizing controller for the safety embedded system guarantees the safe stabilization of the original safety-critical system, effectively mitigating conflicts between performance and safety constraints. This approach enables the use of various legacy control methods from the literature to develop safe control laws. Moreover, it explores how this method can be applied to enforce input constraints and extend traditional control techniques to incorporate safety considerations. Additionally, the paper introduces input-to-state safety (ISSf) through barrier states for analyzing robust safety under bounded input disturbances and develops the notion of input-to-state safe stability IS3 for analyzing and designing robustly safe stabilizing feedback controls. The proposed techniques and concepts are used in various examples including the design of proportional-integral-derivative-barrier (PIDB) control for adaptive cruise control.

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arXiv2025

LLA-MPC: Fast Adaptive Control for Autonomous Racing

We present Look-Back and Look-Ahead Adaptive Model Predictive Control (LLA-MPC), a real-time adaptive control framework for autonomous racing that addresses the challenge of rapidly changing tire-surface interactions. Unlike existing approaches requiring substantial data collection or offline training, LLA-MPC employs a model bank for immediate adaptation without a learning period. It integrates two key mechanisms: a look-back window that evaluates recent vehicle behavior to select the most accurate model and a look-ahead horizon that optimizes trajectory planning based on the identified dynamics. The selected model and estimated friction coefficient are then incorporated into a trajectory planner to optimize reference paths in real-time. Experiments across diverse racing scenarios demonstrate that LLA-MPC outperforms state-of-the-art methods in adaptation speed and handling, even during sudden friction transitions. Its learning-free, computationally efficient design enables rapid adaptation, making it ideal for high-speed autonomous racing in multi-surface environments.

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arXiv2025

Safety Embedded Adaptive Control Using Barrier States

In this work, we explore the application of barrier states (BaS) in the realm of safe nonlinear adaptive control. Our proposed framework derives barrier states for systems with parametric uncertainty, which are augmented into the uncertain dynamical model. We employ an adaptive nonlinear control strategy based on a control Lyapunov functions approach to design a stabilizing controller for the augmented system. The developed theory shows that the controller ensures safe control actions for the original system while meeting specified performance objectives. We validate the effectiveness of our approach through simulations on diverse systems, including a planar quadrotor subject to unknown drag forces and an adaptive cruise control system, for which we provide comparisons with existing methodologies.

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arXiv2024

Differentiable Robust Model Predictive Control

Deterministic model predictive control (MPC), while powerful, is often insufficient for effectively controlling autonomous systems in the real-world. Factors such as environmental noise and model error can cause deviations from the expected nominal performance. Robust MPC algorithms aim to bridge this gap between deterministic and uncertain control. However, these methods are often excessively difficult to tune for robustness due to the nonlinear and non-intuitive effects that controller parameters have on performance. To address this challenge, we first present a unifying perspective on differentiable optimization for control using the implicit function theorem (IFT), from which existing state-of-the art methods can be derived. Drawing parallels with differential dynamic programming, the IFT enables the derivation of an efficient differentiable optimal control framework. The derived scheme is subsequently paired with a tube-based MPC architecture to facilitate the automatic and real-time tuning of robust controllers in the presence of large uncertainties and disturbances. The proposed algorithm is benchmarked on multiple nonlinear robotic systems, including two systems in the MuJoCo simulator environment and one hardware experiment on the Robotarium testbed, to demonstrate its efficacy.

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arXiv2024

Improved Exploration for Safety-Embedded Differential Dynamic Programming Using Tolerant Barrier States

In this paper, we introduce Tolerant Discrete Barrier States (T-DBaS), a novel safety-embedding technique for trajectory optimization with enhanced exploratory capabilities. The proposed approach generalizes the standard discrete barrier state (DBaS) method by accommodating temporary constraint violation during the optimization process while still approximating its safety guarantees. Consequently, the proposed approach eliminates the DBaS's safe nominal trajectories assumption, while enhancing its exploration effectiveness for escaping local minima. Towards applying T-DBaS to safety-critical autonomous robotics, we combine it with Differential Dynamic Programming (DDP), leading to the proposed safe trajectory optimization method T-DBaS-DDP, which inherits the convergence and scalability properties of the solver. The effectiveness of the T-DBaS algorithm is verified on differential drive robot and quadrotor simulations. In addition, we compare against the classical DBaS-DDP as well as Augmented-Lagrangian DDP (AL-DDP) in extensive numerical comparisons that demonstrate the proposed method's competitive advantages. Finally, the applicability of the proposed approach is verified through hardware experiments on the Georgia Tech Robotarium platform.

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arXiv2023

Safe Importance Sampling in Model Predictive Path Integral Control

We introduce the notion of importance sampling under embedded barrier state control, titled Safety Controlled Model Predictive Path Integral Control (SC-MPPI). For robotic systems operating in an environment with multiple constraints, hard constraints are often encoded utilizing penalty functions when performing optimization. Alternative schemes utilizing optimization-based techniques, such as Control Barrier Functions, can be used as a safety filter to ensure the system does not violate the given hard constraints. In contrast, this work leverages the principle of a safety filter but applies it during forward sampling for Model Predictive Path Integral Control. The resulting set of forward samples can remain safe within the domain of the safety controller, increasing sample efficiency and allowing for improved exploration of the state space. We derive this controller through information theoretic principles analogous to Information Theoretic MPPI. We empirically demonstrate both superior sample efficiency, exploration, and system performance of SC-MPPI when compared to Model-Predictive Path Integral Control (MPPI) and Differential Dynamic Programming (DDP) optimizing the barrier state.

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arXiv2022

Gaussian Process Barrier States for Safe Trajectory Optimization and Control

This paper proposes embedded Gaussian Process Barrier States (GP-BaS), a methodology to safely control unmodeled dynamics of nonlinear system using Bayesian learning. Gaussian Processes (GPs) are used to model the dynamics of the safety-critical system, which is subsequently used in the GP-BaS model. We derive the barrier state dynamics utilizing the GP posterior, which is used to construct a safety embedded Gaussian process dynamical model (GPDM). We show that the safety-critical system can be controlled to remain inside the safe region as long as we can design a controller that renders the BaS-GPDM's trajectories bounded (or asymptotically stable). The proposed approach overcomes various limitations in early attempts at combining GPs with barrier functions due to the abstention of restrictive assumptions such as linearity of the system with respect to control, relative degree of the constraints and number or nature of constraints. This work is implemented on various examples for trajectory optimization and control including optimal stabilization of unstable linear system and safe trajectory optimization of a Dubins vehicle navigating through an obstacle course and on a quadrotor in an obstacle avoidance task using GP differentiable dynamic programming (GP-DDP). The proposed framework is capable of maintaining safe optimization and control of unmodeled dynamics and is purely data driven.

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arXiv2022

Sampling-Based Optimization for Multi-Agent Model Predictive Control

We systematically review the Variational Optimization, Variational Inference and Stochastic Search perspectives on sampling-based dynamic optimization and discuss their connections to state-of-the-art optimizers and Stochastic Optimal Control (SOC) theory. A general convergence and sample complexity analysis on the three perspectives is provided through the unifying Stochastic Search perspective. We then extend these frameworks to their distributed versions for multi-agent control by combining them with consensus Alternating Direction Method of Multipliers (ADMM) to decouple the full problem into local neighborhood-level ones that can be solved in parallel. Model Predictive Control (MPC) algorithms are then developed based on these frameworks, leading to fully decentralized sampling-based dynamic optimizers. The capabilities of the proposed algorithms framework are demonstrated on multiple complex multi-agent tasks for vehicle and quadcopter systems in simulation. The results compare different distributed sampling-based optimizers and their centralized counterparts using unimodal Gaussian, mixture of Gaussians, and stein variational policies. The scalability of the proposed distributed algorithms is demonstrated on a 196-vehicle scenario where a direct application of centralized sampling-based methods is shown to be prohibitive.

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arXiv2022

Safety in Augmented Importance Sampling: Performance Bounds for Robust MPPI

This work explores the nature of augmented importance sampling in safety-constrained model predictive control problems. When operating in a constrained environment, sampling based model predictive control and motion planning typically utilizes penalty functions or expensive optimization based control barrier algorithms to maintain feasibility of forward sampling. In contrast the presented algorithm utilizes discrete embedded barrier states in augmented importance sampling to apply feedback with respect to a nominal state when sampling. We will demonstrate that this approach of safety of discrete embedded barrier states in augmented importance sampling is more sample efficient by metric of collision free trajectories, is computationally feasible to perform per sample, and results in better safety performance on a cluttered navigation task with extreme un-modeled disturbances. In addition, we will utilize the theoretical properties of augmented importance sampling and safety control to derive a new bound on the free energy of the system.

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arXiv2022

Barrier States Embedded Iterative Dynamic Game for Robust and Safe Trajectory Optimization

Considering uncertainties and disturbances is an important, yet challenging, step in successful decision making. The problem becomes more challenging in safety-constrained environments. In this paper, we propose a robust and safe trajectory optimization algorithm through solving a constrained min-max optimal control problem. The proposed method leverages a game theoretic differential dynamic programming approach with barrier states to handle parametric and non-parametric uncertainties in safety-critical control systems. Barrier states are embedded into the differential game's dynamics and cost to portray the constrained environment in a higher dimensional state space and certify the safety of the optimized trajectory. Moreover, to find a convergent optimal solution, we propose to perform line-search in a Stackleberg (leader-follower) game fashion instead of picking a constant learning rate. The proposed algorithm is evaluated on a velocity-constrained inverted pendulum model in a moderate and high parametric uncertainties to show its efficacy in such a comprehensible system. The algorithm is subsequently implemented on a quadrotor in a windy environment in which sinusoidal wind turbulences applied in all directions.

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arXiv2022

HJB Based Optimal Safe Control Using Control Barrier Functions

This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of the Hamilton-Jacobi-Bellman (HJB) equation subjected to the safety constraints. By solving the optimization problem, we are able to construct a closed form solution that satisfies optimality and safety conditions. The proposed solution is shown to be continuous and thus it renders the safe set forward invariant while minimizing the given cost. Hence, optimal stabilizability and safety objectives are achieved simultaneously. To synthesize the optimal safe controller, we present a modified Galerkin successive approximation approach which guarantees an optimal safe solution given a stabilizing safe initialization. The proposed algorithm is implemented on a constrained nonlinear system to show its efficacy.

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arXiv2022

Safety Embedded Differential Dynamic Programming Using Discrete Barrier States

Certified safe control is a growing challenge in robotics, especially when performance and safety objectives must be concurrently achieved. In this work, we extend the barrier state (BaS) concept, recently proposed for safe stabilization of continuous time systems, to safety embedded trajectory optimization for discrete time systems using discrete barrier states (DBaS). The constructed DBaS is embedded into the discrete model of the safety-critical system integrating safety objectives into the system's dynamics and performance objectives. Thereby, the control policy is directly supplied by safety-critical information through the barrier state. This allows us to employ the DBaS with differential dynamic programming (DDP) to plan and execute safe optimal trajectories. The proposed algorithm is leveraged on various safety-critical control and planning problems including a differential wheeled robot safe navigation in randomized and complex environments and on a quadrotor to safely perform reaching and tracking tasks. The DBaS-based DDP (DBaS-DDP) is shown to consistently outperform penalty methods commonly used to approximate constrained DDP problems as well as CBF-based safety filters.

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arXiv2021

Safety Embedded Control of Nonlinear Systems via Barrier States

In many safety-critical control systems, possibly opposing safety restrictions and control performance objectives arise. To confront such a conflict, this letter proposes a novel methodology that embeds safety into stability of control systems. The development enforces safety by means of barrier functions used in optimization through the construction of barrier states (BaS) which are embedded in the control system's model. As a result, as long as the equilibrium point of interest of the closed loop system is asymptotically stable, the generated trajectories are guaranteed to be safe. Consequently, a conflict between control objectives and safety constraints is substantially avoided. To show the efficacy of the proposed technique, we employ barrier states with the simple pole placement method to design safe linear controls. Nonlinear optimal control is subsequently employed to fulfill safety, stability and performance objectives by solving the associated Hamilton-Jacobi-Bellman (HJB) which minimizes a cost functional that can involve the BaS. Following this further, we exploit optimal control with barrier states on an unstable, constrained second dimensional pendulum on a cart model that is desired to avoid low velocities regions where the system may exhibit some controllability loss and on two mobile robots to safely arrive to opposite targets with an obstacle on the way.

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arXiv2020

Recursive Analytic Solution of Nonlinear Optimal Regulators

The paper develops an optimal regulator for a general class of multi-input affine nonlinear systems minimizing a nonlinear cost functional with infinite horizon. The cost functional is general enough to enforce saturation limits on the control input if desired. An efficient algorithm utilizing tensor algebra is employed to compute the tensor coefficients of the Taylor series expansion of the value function (i.e., optimal cost-to-go). The tensor coefficients are found by solving a set of nonlinear matrix equations recursively generalizing the well-known linear quadratic solution. The resulting solution generates the optimal controller as a nonlinear function of the state vector up to a prescribed truncation order. Moreover, a complete convergence of the computed solution together with an estimation of its applicability domain are provided to further guide the user. The algorithm's computational complexity is shown to grow only polynomially with respect to the series order. Finally, several nonlinear examples including some with input saturation are presented to demonstrate the efficacy of the algorithm to generate high order Taylor series solution of the optimal controller.

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