@inproceedings{24_gao_realtimefeasible,

title = {Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects},

author = {Yunfan Gao and Florian Messerer and Niels van Duijkeren and Boris Houska and Moritz Diehl},

doi = {https://doi.org/10.48550/arXiv.2409.12007},

year  = {2024},

date = {2024-09-18},

abstract = {Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not overlap if and only if the endpoint of the vector between the center points of the ellipsoids does not lie in the interior of the Minkowski sum of the ellipsoids. This condition is formulated using a parametric over-approximation of the Minkowski sum, which can be made tight in any given direction. The resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.},

note = {Accepted at the 2024 Conference on Decision and Control (CDC)},

keywords = {},

pubstate = {forthcoming},

tppubtype = {inproceedings}

}

@inproceedings{24_gao_stochasticmpc,

title = {Stochastic Model Predictive Control with Optimal Linear Feedback for Mobile Robots in Dynamic Environments},

author = {Yunfan Gao and Florian Messerer and Niels van Duijkeren and Moritz Diehl},

doi = {https://doi.org/10.1016/j.ifacol.2024.09.024},

year  = {2024},

date = {2024-09-03},

urldate = {2024-09-03},

booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},

volume = {58},

number = {18},

pages = {153-158},

publisher = {IFAC-PapersOnLine},

abstract = {Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to take place. In this paper, to counteract the rapidly growing human motion uncertainty over time, we incorporate state feedback in the stochastic MPC. This allows the robot to more closely track reference trajectories. To this end the feedback policy is left as a degree of freedom in the optimal control problem. The stochastic MPC with feedback is validated in simulation experiments and is compared against nominal MPC and stochastic MPC without feedback. The added computation time can be limited by reducing the number of additional variables for the feedback law with a small compromise in control performance.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{leeman_fast_2024,

title = {Fast System Level Synthesis: Robust Model Predictive Control Using Riccati Recursions},

author = {Antoine P. Leeman and Johannes Köhler and Florian Messerer and Amon Lahr and Moritz Diehl and Melanie N. Zeilinger},

url = {https://doi.org/10.48550/arXiv.2401.13762},

doi = {10.1016/j.ifacol.2024.09.027},

year  = {2024},

date = {2024-09-01},

urldate = {2024-02-07},

booktitle = {8th IFAC Conference on Nonlinear Model Predictive Control NMPC 2024},

volume = {58},

number = {18},

publisher = {IFAC-PapersOnLine},

abstract = {System Level Synthesis (SLS) enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem. The proposed algorithm builds on a recently proposed joint optimization scheme and iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of O(N2(n3x+n3u)) for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups of order 10 to 10^3 compared to general-purpose commercial solvers.

},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{frey_efficient_2023,

title = {Efficient Zero-Order Robust Optimization for Real-Time Model Predictive Control with Acados},

author = {Jonathan Frey and Yunfan Gao and Florian Messerer and Amon Lahr and Melanie N. Zeilinger and Moritz Diehl},

doi = {10.23919/ECC64448.2024.10591148},

isbn = {978-3-9071-4410-7},

year  = {2024},

date = {2024-06-03},

urldate = {2023-12-18},

booktitle = {2024 European Control Conference (ECC)},

publisher = {IEEE},

address = {Stockholm, Sweden},

abstract = {Robust and stochastic optimal control problem (OCP) formulations allow a systematic treatment of uncertainty, but are typically associated with a high computational cost. The recently proposed zero-order robust optimization (zoRO) algorithm mitigates the computational cost of uncertainty-aware MPC by propagating the uncertainties separately from the nominal dynamics. This paper details the combination of zoRO with the real-time iteration (RTI) scheme and presents an efficient open-source implementation in acados, utilizing BLASFEO for the linear algebra operations. In addition to the scaling advantages posed by the zoRO algorithm, the efficient implementation drastically reduces the computational overhead, and, combined with an RTI scheme, enables the use of tube-based MPC for a wider range of applications. The flexibility, usability and effectiveness of the proposed implementation is demonstrated on two examples. On the practical example of a differential drive robot, the proposed implementation results in a tenfold reduction of computation time with respect to the previously available zoRO implementation.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{GaoCFMPECC23,

title = {Collision-free Motion Planning for Mobile Robots by Zero-order Robust Optimization-based MPC},

author = {Yunfan Gao and Florian Messerer and Jonathan Frey and Niels Duijkeren and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/10178311},

doi = {https://doi.org/10.23919/ECC57647.2023.10178311},

isbn = {978-3-907144-08-4},

year  = {2023},

date = {2023-07-17},

urldate = {2023-07-17},

booktitle = {2023 European Control Conference (ECC)},

pages = {1-6},

publisher = {IEEE},

address = {Bucharest, Romania},

abstract = {This paper presents an implementation of robust model predictive control (MPC) for collision-free reference trajectory tracking for mobile robots. The presented approach considers the robot motion to be subject to process noise bounded by ellipsoidal sets. In order to efficiently handle the evolution of the disturbance ellipsoids within the MPC, the zero-order robust optimization (zoRO) scheme is applied [1]. The idea is to fix the disturbance ellipsoids within one optimization iteration and solve the problem repeatedly with updated disturbance ellipsoid trajectories. The zero-order approach is suboptimal in general. However, we show that it does not impair convergence to the reference trajectory in the absence of obstacles. The experiments on an industrial mobile robot prototype demonstrate the performance of the controller.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{Baumgaertner2023a,

title = {A Unified Local Convergence Analysis of Differential Dynamic Programming, Direct Single Shooting, and Direct Multiple Shooting},

author = {Katrin Baumgärtner and Florian Messerer and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/10178367},

doi = {https://doi.org/10.23919/ECC57647.2023.10178367},

isbn = {978-3-907144-08-4},

year  = {2023},

date = {2023-07-17},

urldate = {2023-07-17},

booktitle = {2023 European Control Conference (ECC)},

pages = {1-7},

publisher = {IEEE},

address = {Bucharest, Romania},

abstract = {We revisit three classical numerical methods for solving unconstrained optimal control problems - differential dynamic programming, direct single shooting, and direct multiple shooting - and examine their local convergence behaviour. In particular, we show that all three methods converge with the same linear rate if a Gauss-Newton (GN) - or Generalized Gauss-Newton (GGN) - Hessian approximation is used, which is the case in widely used implementations such as iLQR.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}

@inproceedings{reiter_inverse_2022,

title = {An Inverse Optimal Control Approach for Trajectory Prediction of Autonomous Race Cars},

author = {Rudolf Reiter and Florian Messerer and Markus Schratter and Daniel Watzenig and Moritz Diehl},

url = {https://ieeexplore.ieee.org/document/9838100/},

doi = {10.23919/ECC55457.2022.9838100},

isbn = {978-3-907144-07-7},

year  = {2022},

date = {2022-07-01},

urldate = {2022-09-09},

booktitle = {2022 European Control Conference (ECC)},

pages = {146--153},

publisher = {IEEE},

address = {London, United Kingdom},

abstract = {This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk smoothness, and which is restricted by constraints. The algorithm predicts a trajectory by solving a parameterized nonlinear program (NLP) which contains path progress and smoothness in cost terms. By observing the actual motion of a vehicle, the parameters of prediction are updated by means of solving an inverse optimal control problem that contains the parameters of the predicting NLP as optimization variables. The algorithm therefore learns to predict the observed vehicle trajectory in a least-squares relation to measurement data and to the presumed structure of the predicting NLP. This work contributes with an algorithm that allows for accurate and interpretable predictions with sparse data. The algorithm is implemented on embedded hardware in an autonomous real-world race car that is competing in the challenge Roborace and analyzed with respect to recorded data.},

keywords = {},

pubstate = {published},

tppubtype = {inproceedings}

}