Abstract

Robotic magnetic manipulation offers a minimally invasive approach to gastrointestinal examinations through capsule endoscopy. However, controlling such systems using external permanent magnets (EPM) is challenging due to nonlinear magnetic interactions, especially when there are complex navigation requirements such as avoidance of sensitive tissues. In this work, we present a novel trajectory planning and control method incorporating dynamics and navigation requirements, using a single EPM fixed to a robotic arm to manipulate an internal permanent magnet (IPM). Our approach employs a constrained iterative linear quadratic regulator that considers the dynamics of the IPM to generate optimal trajectories for both the EPM and IPM. Extensive simulations and real-world experiments, motivated by capsule endoscopy operations, demonstrate the robustness of the method, showcasing resilience to external disturbances and precise control under varying conditions. The experimental results show that the IPM reaches the goal position with a maximum mean error of 0.18 cm and a standard deviation of 0.21 cm. This work introduces a unified framework for constrained trajectory optimization in magnetic manipulation, directly incorporating both the IPM’s dynamics and the EPM’s manipulability.

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Abstract

Hybrid dynamical systems pose significant challenges for effective planning and control, especially when additional constraints such as obstacle avoidance, state boundaries, and actuation limits are present. In this letter, we extend the recently proposed Hybrid iLQR method [1] to handle state and input constraints within an indirect optimization framework, aiming to preserve computational efficiency and ensure dynamic feasibility. Specifically, we incorporate two constraint handling mechanisms into the Hybrid iLQR: Discrete Barrier State and Augmented Lagrangian methods. Comprehensive simulations across various operational situations are conducted to evaluate and compare the performance of these extended methods in terms of convergence and their ability to handle infeasible starting trajectories. Results indicate that while the Discrete Barrier State approach is more computationally efficient, the Augmented Lagrangian method outperforms it in complex and real-world scenarios with infeasible initial trajectories.

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Abstract

Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel and computationally efficient approach for trajectory optimization on matrix Lie groups using an augmented Lagrangian-based constrained discrete Differential Dynamic Programming (DDP). The method involves lifting the optimization problem to the Lie algebra during the backward pass and retracting back to the manifold during the forward pass. Unlike previous approaches that addressed constraint handling only for specific classes of matrix Lie groups, the proposed method provides a general solution for nonlinear constraint handling across generic matrix Lie groups. We evaluate the effectiveness of the proposed DDP method in handling constraints within a mechanical system characterized by rigid body dynamics in SE(3), assessing its computational efficiency compared to existing direct optimization solvers. Additionally, the method demonstrates robustness under external disturbances when applied as a Lie-algebraic feedback control policy on SE(3), and in optimizing a quadrotor’s trajectory in a challenging realistic scenario. Experiments show that the proposed approach effectively manages general constraints defined on configuration, velocity, and inputs during optimization, while also maintaining stability under external disturbances when executing the resultant control policy in closed-loop.

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Keywords

• Matrix Lie Groups
• Geometric Control
• Trajectory Optimization
• Constrained Optimization
• Differential Dynamic Programming

BibTeX

@article{alcan2024cddplie,
  title={Constrained Trajectory Optimization on Matrix Lie Groups via Lie-Algebraic Differential Dynamic Programming},
  author={Alcan, Gokhan and Abu-Dakka, Fares J and Kyrki, Ville},
  journal={arXiv preprint arXiv:2301.02018},
  year={2024}
}

Safety-critical traffic scenarios are integral to the development and validation of autonomous driving systems. These scenarios provide crucial insights into vehicle responses under high-risk conditions rarely encountered in real-world settings. Recent advancements in critical scenario generation have demonstrated the superiority of diffusion-based approaches over traditional generative models in terms of effectiveness and realism. However, current diffusion-based methods fail to adequately address the complexity of driver behavior and traffic density information, both of which significantly influence driver decision-making processes. In this work, we present a novel approach to overcome these limitations by introducing adversarial guidance functions for diffusion models that incorporate behavior complexity and traffic density, thereby enhancing the generation of more effective and realistic safety-critical traffic scenarios. The proposed method is evaluated on two evaluation metrics: effectiveness and realism.

Abstract

Inverse reinforcement learning (IRL) is an imitation learning approach to learning reward functions from expert demonstrations. Its use avoids the difficult and tedious procedure of manual reward specification while retaining the generalization power of reinforcement learning. In IRL, the reward is usually represented as a linear combination of features. In continuous state spaces, the state variables alone are not sufficiently rich to be used as features, but which features are good is not known in general. To address this issue, we propose a method that employs polynomial basis functions to form a candidate set of features, which are shown to allow the matching of statistical moments of state distributions. Feature selection is then performed for the candidates by leveraging the correlation between trajectory probabilities and feature expectations. We demonstrate the approach’s effectiveness by recovering reward functions that capture expert policies across non-linear control tasks of increasing complexity.

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Overtaking on two-lane roads is a great challenge for autonomous vehicles, as oncoming traffic appearing on the opposite lane may require the vehicle to change its decision and abort the overtaking. Deep reinforcement learning (DRL) has shown promise for difficult decision problems such as this, but it requires massive number of data, especially if the action space is continuous. This paper proposes to incorporate guidance from an expert system into DRL to increase its sample efficiency in the autonomous overtaking setting. The guidance system developed in this study is composed of constrained iterative LQR and PID controllers. The novelty lies in the incorporation of a fading guidance function, which gradually decreases the effect of the expert system, allowing the agent to initially learn an appropriate action swiftly and then improve beyond the performance of the expert system. This approach thus combines the strengths of traditional control engineering with the flexibility of learning systems, expanding the capabilities of the autonomous system. The proposed methodology for autonomous vehicle overtaking does not depend on a particular DRL algorithm and three state-of-the-art algorithms are used as baselines for evaluation. Simulation results show that incorporating expert system guidance improves state-of-the-art DRL algorithms greatly in both sample efficiency and driving safety.

Autonomous vehicles are a growing technology that aims to enhance safety, accessibility, efficiency, and convenience through autonomous maneuvers ranging from lane change to overtaking. Overtaking is one of the most challenging maneuvers for autonomous vehicles, and current techniques for autonomous overtaking are limited to simple situations. This paper studies how to increase safety in autonomous overtaking by allowing the maneuver to be aborted. We propose a decision-making process based on a deep Q-Network to determine if and when the overtaking maneuver needs to be aborted. The proposed algorithm is empirically evaluated in simulation with varying traffic situations, indicating that the proposed method improves safety during overtaking maneuvers. Furthermore, the approach is demonstrated in real-world experiments using the autonomous shuttle iseAuto.