I.Z. El-Hajj
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This paper presents a reachability-guided controller for nonlinear systems that synthesizes pseudo-optimal control using only local linear models. At each step, a forward reachable tube (FRT) is computed via zonotope-based set propagation; the closest point in the FRT to the target is chosen as an intermediate waypoint, around which a backward reachable tube (BRT) is solved using Hamilton–Jacobi (HJ) reachability. The resulting value function yields a locally optimal control action. This process is repeated iteratively to steer the system toward the target without requiring global nonlinear dynamics. We evaluate the method on the double integrator, inverted pendulum, and Dubins car, benchmarking against model predictive control baselines. For the double integrator, we additionally benchmark against its ground-truth time-optimal bang-bang solution. Our proposed ZonoReach controller achieves successful setpoint tracking and near time-optimal performance. Results highlight the influence of planning and control horizons, while limitations include reliance on local linear approximations and grid-based solvers for BRT computation. We conclude with directions for improving scalability toward real-world systems.
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This paper presents a reachability-guided controller for nonlinear systems that synthesizes pseudo-optimal control using only local linear models. At each step, a forward reachable tube (FRT) is computed via zonotope-based set propagation; the closest point in the FRT to the target is chosen as an intermediate waypoint, around which a backward reachable tube (BRT) is solved using Hamilton–Jacobi (HJ) reachability. The resulting value function yields a locally optimal control action. This process is repeated iteratively to steer the system toward the target without requiring global nonlinear dynamics. We evaluate the method on the double integrator, inverted pendulum, and Dubins car, benchmarking against model predictive control baselines. For the double integrator, we additionally benchmark against its ground-truth time-optimal bang-bang solution. Our proposed ZonoReach controller achieves successful setpoint tracking and near time-optimal performance. Results highlight the influence of planning and control horizons, while limitations include reliance on local linear approximations and grid-based solvers for BRT computation. We conclude with directions for improving scalability toward real-world systems.
Conference paper
(2018)
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Svenja Woicke, Andres S. Moreno Gonzalez, Isabelle El-Hajj, Jelle W.F. Mes, Martin Henkel, R. S.D. Autar, Robert A. Klavers
Precise landings on other bodies require more than just dead reckoning using an inertial measurement unit on-board the lander. If navigation of the lander with respect to a planetary surface is desired, so-called crater detection and crater-matching algorithms might be a valuable asset to find the inertial position of the vehicle using terrain relative navigation techniques. This would enable landing close to an inertially defined landing site, which could, for example, be a surface asset of a previous mission. With the desire to reduce the landing ellipse size, more precise knowledge of the inertial state of the lander is required. Based on an extensive literature review, six different algorithms were implemented to assess the performance of these. This assessment will aid the selection of crater-detection techniques for future precision landing missions. To compare the different algorithms trade-off criteria have been established. The following criteria are assessed: 1) True detection rates 2) False detection rates 3) Accuracy: as the reference maps usually have rather high resolution, inaccuracies of just a few pixels can cause large errors. 4) Run-time: the algorithm should be on-board capable. Moreover, the robustness of the algorithms was investigated. It was found that all algorithms are capable of performing the task of extracting sufficient craters for localising the landing vehicle with respect to a surface map. A method based on extracting and clustering lit pixels delivered the most promising results for the overall detections, whereas, the machine-learning based algorithms showed slightly better robustness.
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Precise landings on other bodies require more than just dead reckoning using an inertial measurement unit on-board the lander. If navigation of the lander with respect to a planetary surface is desired, so-called crater detection and crater-matching algorithms might be a valuable asset to find the inertial position of the vehicle using terrain relative navigation techniques. This would enable landing close to an inertially defined landing site, which could, for example, be a surface asset of a previous mission. With the desire to reduce the landing ellipse size, more precise knowledge of the inertial state of the lander is required. Based on an extensive literature review, six different algorithms were implemented to assess the performance of these. This assessment will aid the selection of crater-detection techniques for future precision landing missions. To compare the different algorithms trade-off criteria have been established. The following criteria are assessed: 1) True detection rates 2) False detection rates 3) Accuracy: as the reference maps usually have rather high resolution, inaccuracies of just a few pixels can cause large errors. 4) Run-time: the algorithm should be on-board capable. Moreover, the robustness of the algorithms was investigated. It was found that all algorithms are capable of performing the task of extracting sufficient craters for localising the landing vehicle with respect to a surface map. A method based on extracting and clustering lit pixels delivered the most promising results for the overall detections, whereas, the machine-learning based algorithms showed slightly better robustness.