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 augmented Lagrangian-based constrained Differential Dynamic Programming (DDP) approach specifically designed for trajectory optimization on matrix Lie groups. Our method formulates the optimization problem in the error-state space, employs automatic differentiation during the backward pass, and ensures manifold consistency through discrete-time Lie-group integration during the forward pass. Unlike previous methods limited to specific manifold classes, our approach robustly handles generic nonlinear constraints across arbitrary matrix Lie groups and exhibits resilience to constraint violations during training. We evaluate the proposed DDP algorithm through extensive experiments, demonstrating its efficacy in managing constraints within a rigid-body mechanical system on SE(3), its computational superiority compared to existing optimization solvers, robustness under external disturbances as a Lie-algebraic feedback controller, and effectiveness in trajectory optimization tasks including realistic quadrotor scenarios as underactuated systems and deformable objects whose deformation dynamics are represented in SL(2). The experimental results validate the generality, stability, and computational efficiency of our proposed method.

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Keywords

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

BibTeX

@article{alcan2025cddplie,
  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={Systems & Control Letters},
  volume={204},
  year={2025}
}

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

Realistic physics engines play a crucial role for learning to manipulate deformable objects such as garments in simulation. By doing so, researchers can circumvent challenges such as sensing the deformation of the object in the real-world. In spite of the extensive use of simulations for this task, few works have evaluated the reality gap between deformable object simulators and real-world data. We present a benchmark dataset to evaluate the sim-to-real gap in cloth manipulation. The dataset is collected by performing a dynamic cloth manipulation task involving contact with a rigid table. We use the dataset to evaluate the reality gap, computational time, and simulation stability of four popular deformable object simulators: MuJoCo, Bullet, Flex, and SOFA. Additionally, we discuss the benefits and drawbacks of each simulator.

>Project Website<

Keywords

• Datasets for Robot Learning
• Bimanual Manipulation
• Deformable Object Manipulation

BibTeX

@article{blanco2024benchmarking,
  title={Benchmarking the sim-to-real gap in cloth manipulation},
  author={Blanco-Mulero, David and Barbany, Oriol and Alcan, Gokhan and Colom{\'e}, Adri{\`a} and Torras, Carme and Kyrki, Ville},
  journal={IEEE Robotics and Automation Letters},
  volume={9}, 
  number={3}, 
  pages={1760--1767},
  year={2024},
  publisher={IEEE}
}

Abstract

In this paper, optimization-oriented high fidelity indicated torque models which cover the whole operating regions under both steady-state and transient cycles for heavy-duty vehicles are developed. Two different experiments are performed and their data are merged to be utilized in the training of the models. In the first experiment, all combustion input channels are excited by quadratic chirp signals with different sweeps in their frequency profiles. Different from the first experiment, the engine speed is excited by ramp-hold signals in the second experiment. The estimations of friction, pumping and inertia torques in addition to the torque measured from the engine dynamometer are utilized in the indicated torque calculations. In order to model the calculated indicated torque, a nonlinear finite impulse response (NFIR) model with a single layer sigmoid neural network has been designed. A sensitivity analysis is performed by generating several models with different number of input regressors and neurons. Experimental results show that the majority of the models in a selected wide range of the model parameters are validated with fit accuracies higher than 90 % and 85 % on the World Harmonized Stationary Cycle (WHSC) and the World Harmonic Transient Cycle (WHTC), respectively.

Keywords

• • Diesel engine
  • Indicated torque
  • System identification
  • Experiment design
  • NFIR model

BibTeX

@article{alcan2020optimization,
  title={Optimization-oriented high fidelity NFIR models for estimating indicated torque in diesel engines},
  author={Alcan, Gokhan and Aran, Volkan and Unel, Mustafa and Yilmaz, Metin and Gurel, Cetin and Koprubasi, Kerem},
  journal={International Journal of Automotive Technology},
  volume={21},
  number={3},
  pages={729--737},
  year={2020},
  publisher={The Korean Society of Automotive Engineers}
}

Abstract

In this work, acceleration feedback is utilized in a hierarchical control structure for robust trajectory control of a quadrotor helicopter subject to external disturbances where reference attitude angles are determined through a nonlinear optimization algorithm. Furthermore, an acceleration-based disturbance observer (AbDOB) is designed to estimate disturbances acting on the positional dynamics of the quadrotor. For the attitude control, nested position, velocity, and inner acceleration feedback loops consisting of PID and PI type controllers are developed to provide high stiffness against external disturbances. Reliable angular acceleration is estimated through a cascaded filter structure. Simulation results show that the proposed controllers provide robust trajectory tracking performance when the aerial vehicle is subject to wind gusts generated by the Dryden wind model along with the uncertainties and measurement noise. Results also demonstrate that the reference attitude angles calculated through nonlinear optimization are smooth and within the desired bounds.

Keywords

• Robust Control
• Acceleration Feedback
• Disturbance Observer
• Quadrotor
• Hierarchical Control
• Nonlinear Optimization

BibTeX

@article{zaki2019robust,
  title={Robust trajectory control of an unmanned aerial vehicle using acceleration feedback},
  author={Zaki, Hammad and Alcan, Gokhan and Unel, Mustafa},
  journal={International Journal of Mechatronics and Manufacturing Systems},
  volume={12},
  number={3-4},
  pages={298--317},
  year={2019},
  publisher={Inderscience Publishers (IEL)}
}

Abstract

Diesel engines are still widely used in heavy-duty engine industry because of their high energy conversion efficiency. In recent decades, governmental institutions limit the maximum acceptable hazardous emissions of diesel engines by stringent international regulations, which enforces engine manufacturers to find a solution for reducing the emissions while keeping the power requirements. A reliable model of the diesel engine combustion process can be quite useful to search for the best engine operating conditions. In this study, nonlinear modeling of a heavy-duty diesel engine NOx emission formation is presented. As a new experiment design, air-path and fuel-path input channels were excited by chirp signals where the frequency profile of each channel is different in terms of the number and the direction of the sweeps. This method is proposed as an alternative to the steady-state experiment design based modeling approach to substantially reduce testing time and improve modeling accuracy in transient operating conditions. Sigmoid based nonlinear autoregressive with exogenous input (NARX) model is employed to predict NOx emissions with given input set under both steady-state and transient cycles. Models for different values of parameters are generated to analyze the sensitivity to parameter changes and a parameter selection method using an easy-to-interpret map is proposed to find the best modeling parameters. Experimental results show that the steady-state and the transient validation accuracies for the majority of the obtained models are higher than 80% and 70%, respectively.

Highlights

• Data-driven modeling of diesel engine NOx emissions using sigmoid NARX model.
• A new design of experiments which include both chirp and ramp-hold signals.
• Reduction of testing time and improved modeling accuracy in transient cycle.
• An easy-to-interpret map as a convenient means for suitable parameter selection.
• Higher than 80% and 70% steady-state and transient validation accuracies.

Keywords

• Diesel engine
• Combustion process
• NOx emissions
• Experiment design
• Sigmoid NARX model

BibTeX

@article{alcan2019predicting,
  title={Predicting NOx emissions in diesel engines via sigmoid NARX models using a new experiment design for combustion identification},
  author={Alcan, Gokhan and Unel, Mustafa and Aran, Volkan and Yilmaz, Metin and Gurel, Cetin and Koprubasi, Kerem},
  journal={Measurement},
  volume={137},
  pages={71--81},
  year={2019},
  publisher={Elsevier}
}

Abstract

This study presents a biomedical device prototype based on small scale hydrodynamic cavitation. The application of small scale hydrodynamic cavitation and its integration to a biomedical device prototype is offered as an important alternative to other techniques, such as ultrasound therapy, and thus constitutes a local, cheap, and energy-efficient solution, for urinary stone therapy and abnormal tissue ablation (e.g., benign prostate hyperplasia (BPH)). The destructive nature of bubbly, cavitating, flows was exploited, and the potential of the prototype was assessed and characterized. Bubbles generated in a small flow restrictive element (micro-orifice) based on hydrodynamic cavitation were utilized for this purpose. The small bubbly, cavitating, flow generator (micro-orifice) was fitted to a small flexible probe, which was actuated with a micromanipulator using fine control. This probe also houses an imaging device for visualization so that the emerging cavitating flow could be locally targeted to the desired spot. In this study, the feasibility of this alternative treatment method and its integration to a device prototype were successfully accomplished.

BibTeX

@article{ghorbani2018biomedical,
  title={Biomedical device prototype based on small scale hydrodynamic cavitation},
  author={Ghorbani, Morteza and Sozer, Canberk and Alcan, Gokhan and Unel, Mustafa and Ekici, Sinan and Uvet, Huseyin and Kosar, Ali},
  journal={AIP Advances},
  volume={8},
  number={3},
  pages={035108},
  year={2018},
  publisher={AIP Publishing}
}