Dual Quaternion-Based Powered Descent Guidance with State-Triggered Constraints

Reynolds, Taylor P.; Szmuk, Michael; Malyuta, Danylo; Mesbahi, Mehran; Açıkmeşe, Behçet; Carson, John M.

doi:10.2514/1.g004536

Cited by 74 publications

(29 citation statements)

References 59 publications

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“…Different from the trust‐region radius adjustment strategies proposed in the literature, 8,11 this modified trust‐region constraint does not need to compute the ratio that decide to shrink or enlarge the radius, also circumvents solving the optimization problem whose solution is rejected. Furthermore, due to the inheriting of Chebyshev norm in the modified trust‐region, it introduces fewer decision variables and constraints in compare to the quadratic adaptive trust region, 9,12 and reduces the computation burden consequently.…”

Section: Hp‐pseudospectral Sequential Convex Programmingmentioning

confidence: 99%

“…The time of flight

{\overline{t}}_{f}

can typically be guessed as a function of distance to the target position and flight velocity as:

{\overline{t}}_{f} = \frac{1}{v_{0}} \cdot \sqrt{{(x_{0} - x_{f})}^{2} + {(y_{0} - y_{f})}^{2} + {(z_{0} - z_{f})}^{2}},

where

x_{0}

y_{0}

z_{0}

v_{0}

are the initial position and velocity of the UAV,

x_{f}

y_{f}

z_{f}

are the target position. The straight‐line initialization method is common in the literature of convex optimization‐based methods, and extensive examples have shown rapid convergence 9,10,12 . As shown in the next section, rapid convergence is achieved using the initial nominal trajectory, despite the initial trajectory is far from feasible.…”

Section: Hp‐pseudospectral Sequential Convex Programmingmentioning

confidence: 99%

“…The inherent nonconvex dynamics and constraints in aerospace engineering problems hinder direct applications of convex programming. Lossless convexification 5,6 and successive convexification 7,8 are two creative techniques to handle the nonconvexity; various modifications and improvements on these two techniques have been developed to facilitate real‐time solving aerospace guidance and control problems, such as virtual control, 9 line search, 10 trust‐region radius adjustment, 11 adaptive trust‐region, 12 and so forth. These methods have successfully applied in powered descent landing, 13 hypersonic reentry, 14 rendezvous and proximity, 7 orbit transfer, 15 and cooperative guidance, 16 to name but a few.…”

Section: Introductionmentioning

confidence: 99%

“…Strong duality equivalent is applied to convert the constraints into tractable form for convex programming; no integer variables are introduced in the constraints. A hp‐pseudospectral (hp‐PS) method is adopted to discretize the optimal control problem instead of the discretization method commonly reported in the literature of convex‐optimization‐based methods, such as, Runge–Kutta rule 9,12,17,28 or trapezoidal rule 10,18,20,29 . The hp‐PS, which has been widely applied to solve general optimal control problems, 30‐32 is an extension of the pseudospectral (PS) method; the PS method is a collocation method that achieves high discretization accuracy with fewer nodes 33,34 .…”

Section: Introductionmentioning

confidence: 99%

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Trajectory optimization with obstacles avoidance via strong duality equivalent and hp‐pseudospectral sequential convex programming

Xia

Wang

Gao

2021

Optim Control Appl Methods

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A trajectory optimization algorithm is developed in this article to compute a trajectory that avoids obstacles for an unmanned aerial vehicle and minimize the load factor. Quadratic and polyhedron obstacles are both considered in this article. To satisfy the safety distance requirements in engineering practice, a distance‐based obstacle avoidance constraint is formulated, which restricts the minimum distance that a vehicle can approach the obstacle. Strong duality equivalent converts the constraints into equivalent forms without introducing binary variables. Subsequently, the trajectory optimization problem is numerically solved via a hp‐pseudospectral sequential convex programming method, which iteratively solves a sequence of second‐order cone programming subproblems until convergence is attained. Furthermore, a modified trust‐region constraint and a customized nominal trajectory update rule are proposed to accelerate the convergence of the algorithm. A group of simulations are performed to demonstrate that the algorithm is computationally efficient and capable of generating a trajectory that satisfies safety distance requirements, preventing conservativeness in the trajectory, reducing the incidence of intersample constraints violation.

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Section: Hp‐pseudospectral Sequential Convex Programmingmentioning

confidence: 99%

“…The time of flight

{\overline{t}}_{f}

can typically be guessed as a function of distance to the target position and flight velocity as:

{\overline{t}}_{f} = \frac{1}{v_{0}} \cdot \sqrt{{(x_{0} - x_{f})}^{2} + {(y_{0} - y_{f})}^{2} + {(z_{0} - z_{f})}^{2}},

where

x_{0}

y_{0}

z_{0}

v_{0}

are the initial position and velocity of the UAV,

x_{f}

y_{f}

z_{f}

Section: Hp‐pseudospectral Sequential Convex Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Trajectory optimization with obstacles avoidance via strong duality equivalent and hp‐pseudospectral sequential convex programming

Xia

Wang

Gao

2021

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…However, the choice may come at the expense of increased attitude error. If a specific energy bound must be satisfied, we may explicitly enforce it by adding constraint (28). In the case that a feasible trajectory with an energy upper bound cannot be found, the attitude pointing schedule may need to be relaxed by observing few regions and/or GPs.…”

Section: Fig 13 Rotor Momentummentioning

confidence: 99%

Attitude Trajectory Optimization for Agile Satellites in Autonomous Remote Sensing Constellation

Sin¹,

Nag²,

Ravindra³

et al. 2021

Preprint

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Agile attitude maneuvering maximizes the utility of remote sensing satellite constellations. By taking into account a satellite's physical properties and its actuator specifications, we may leverage the full performance potential of the attitude control system to conduct agile remote sensing beyond conventional slew-and-stabilize maneuvers. Employing a constellation of agile satellites, coordinated by an autonomous and responsive scheduler, can significantly increase overall response rate, revisit time and global coverage for the mission. In this paper, we use recent advances in sequential convex programming (SCP) based trajectory optimization to enable rapid-target acquisition, pointing and tracking capabilities for a scheduler-based constellation. We present two problem formulations. The Minimum-Time Slew Optimal Control Problem determines the minimum time, required energy, and optimal trajectory to slew between any two orientations given nonlinear quaternion kinematics, gyrostat and actuator dynamics, and state/input constraints. By gridding the space of 3D rotations and efficiently solving this problem on the grid, we produce lookup tables or parametric fits off-line that can then be used on-line by a scheduler to compute accurate estimates of minimum-time and maneuver energy for real-time constellation scheduling. The estimates allow an optimization-based scheduler to produce target-remote-sensing and data-downlinking schedules that are dynamically feasible for each satellite and optimal for the constellation. The Minimum-Effort Multi-Target Pointing Optimal Control Problem is used on-line by each satellite to produce continuous attitude-state and control-input trajectories that realize a given schedule while minimizing attitude error and control effort. The optimal trajectory may then be achieved by a low-level tracking controller. This onboard trajectory generation and tracking scheme is possible due to realtime, efficient SCP implementations. We demonstrate our approach with a numerical example that uses simulation data for a reference satellite in Sun-synchronous orbit passing over globallydistributed, Earth-observation targets.

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Joint synthesis of trajectory and controlled invariant funnel for discrete‐time systems with locally Lipschitz nonlinearities

Kim,

Elango,

Açıkmeşe

2024

Intl J Robust & Nonlinear

Self Cite

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This paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (CIF) for locally Lipschitz nonlinear systems subject to bounded disturbances. The CIF synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. In contrast to existing CIF synthesis methods that compute the CIF with a predefined nominal trajectory, our work aims to optimize the nominal trajectory and the CIF jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost‐optimal nominal trajectory. The proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. The trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the CIF. Then, the funnel update step computes the funnel around the nominal trajectory so that the CIF guarantees an invariance property. As a result, with the optimized trajectory and CIF, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. We validate the proposed method via two applications from robotics.

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Dual Quaternion-Based Powered Descent Guidance with State-Triggered Constraints

Cited by 74 publications

References 59 publications

Trajectory optimization with obstacles avoidance via strong duality equivalent and hp‐pseudospectral sequential convex programming

Trajectory optimization with obstacles avoidance via strong duality equivalent and hp‐pseudospectral sequential convex programming

Attitude Trajectory Optimization for Agile Satellites in Autonomous Remote Sensing Constellation

Joint synthesis of trajectory and controlled invariant funnel for discrete‐time systems with locally Lipschitz nonlinearities

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