Flight Testing a Real-Time Direct Collocation Path Planner

Geiger, Brian R.; Horn, Joseph F.; Sinsley, Gregory L.; Ross, James A.; Long, Lyle N.; Niessner, Albert F.

doi:10.2514/1.36533

Cited by 27 publications

(7 citation statements)

References 15 publications

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“…(15)- (18) defined, it is solved recursively, using an update of current position and target position estimates for each iteration. Efficient pseudospectral methods have made real-time solutions of the optimal control problem not only possible, but a topic of great interest [28,30,[44][45][46][47][48]. The methods are treated extensively in [49][50][51][52] and are not re-derived here.…”

Section: Pseudospectral Methodsmentioning

confidence: 99%

“…Several different approaches to solving the dual control problem have been proposed to make the problem more tractable. Geometric considerations on estimation have been removed by focusing simply on "camera-on-target" time or homing, and solved with several methods, such as direct collocation [28,29], neural networks [30], or heuristics [31][32][33]. Others have reduced the problem to one physical dimension, usually mandating a constant closure to a target and controlling in an orthogonal dimension with pure localization [34,35].…”

Section: The Dual Control Problemmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning

Ross

Cobb²,

Baker³

2014

International Journal of Micro Air Vehicles

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A method is presented to simultaneously solve the optimal control problem and the optimal estimation problem for a bearing-only sensor. For bearing-only systems that require a minimum level of certainty in position relative to a source for mission accomplishment, some amount of maneuver is required to measure range. Traditional methods of trajectory optimization and optimal estimation minimize an information metric. This paper proposes constraining the final value of the information states with known time propagation dynamics relative to a given trajectory which allows for attainment of the required level of information with minimal deviation from a general performance index that can be tailored to a specific vehicle. The proposed method does not suffer from compression of the information metric into a scalar, and provides a route that will attain a particular target estimate quality while maneuvering to a desired relative point or set. An algorithm is created to apply the method in real-time, iteratively estimating target position with an Unscented Kalman Filter and updating the trajectory with an efficient pseudospectral method. Methods and tools required for hardware implementation are presented that apply to any real-time optimal control (RTOC) system. The algorithm is validated with both simulation and flight test, autonomously landing a quadrotor on a wire. INTRODUCTIONBearing-only tracking is a classical navigation problem. Many real-world systems depend on angleonly sensors for target state estimation, such as submarines using only passive sonar, high-speed antiradiation missiles (HARM), robots, and unmanned aerial vehicles (UAVs) using images from an optical sensor. The inability to sense range with each measurement, combined with the inherent nonlinearity of the problem make estimation of a target's location and motion problematic. Moving the sensor orthogonal to the line-of-sight (LOS) generates observability for range estimation, and many researchers have pursued optimal methods for trajectory planning in this context [1][2][3][4][5][6]. Optimal trajectory planning of any sort, however, is notoriously difficult to implement for on-line systems (excepting those simple enough to have a closed-form analytical feedback solution). Notably, recent advances in direct optimization through techniques such as pseudospectral methods (PSM) [7][8][9] have increased the efficiency and stability of obtaining a numeric optimal solution to the point where realtime optimal control (RTOC) of systems with moderate speed dynamics is now possible. This paper proposes a new method of approaching the bearing-only trajectory planning problem that enables simultaneous consideration of both the optimal control problem and a system's prescribed final estimation requirements, overcoming the typical limitations of previous approaches which address each requirement separately. The trajectory planning goal is to provide an optimal trajectory for arrival at a point, or set of points, potentially offset from a relative targe...

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Section: Pseudospectral Methodsmentioning

confidence: 99%

Section: The Dual Control Problemmentioning

confidence: 99%

Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning

Ross

Cobb²,

Baker³

2014

International Journal of Micro Air Vehicles

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“…A means to meet this integration mandate is through the use of algorithms that autonomously generate optimal collision avoidance trajectories to satisfy current FAA regulations that mandate passing aircraft meet either a minimum horizontal or vertical separation distance. A number of works have looked at trajectory planning and optimization for air vehicles using optimal control problem formulations Raghunathan [1], Eele [2], Horn [3] and some, such as Geiger [4] have even demonstrated this method in flight on a small-size unmanned vehicle. However, a potential limitation of this method is enforcing conditional inequality constraints such as maintaining either a minimum horizontal or vertical separation distance from an approaching aircraft or complying with FAA right of way (ROW) rules.…”

Section: Introductionmentioning

confidence: 99%

Implementing Conditional Inequality Constraints for Optimal Collision Avoidance

Smith¹,

Arendt²,

Cobb³

et al. 2017

J Aeronaut Aerospace Eng

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Current Federal Aviation Administration regulations require that passing aircraft must either meet a specified horizontal or vertical separation distance. However, solving for optimal avoidance trajectories with conditional inequality path constraints is problematic for gradient-based numerical nonlinear programming solvers since conditional constraints typically possess non-differentiable points. Further, the literature is silent on robust treatment of approximation methods to implement conditional inequality path constraints for gradient-based numerical nonlinear programming solvers. This paper proposes two efficient methods to enforce conditional inequality path constraints in the optimal control problem formulation and compares and contrasts these approaches on representative airborne avoidance scenarios. The first approach is based on a minimum area enclosing superellipse function and the second is based on use of sigmoid functions. These proposed methods are not only robust, but also conservative, that is, their construction is such that the approximate feasible region is a subset of the true feasible region. Further, these methods admit analytically derived bounds for the over-estimation of the infeasible region with a demonstrated maximum error of no greater than 0.3% using the superellipse method, which is less than the resolution of typical sensors used to calculate aircraft position or altitude. However, the superellipse method is not practical in all cases to enforce conditional inequality path constraints that may arise in the nonlinear airborne collision avoidance problem. Therefore, this paper also highlights by example when the use of sigmoid functions are more appropriate.

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“…The constructed NLP problem is typically solved by available solver based on gradient methods 16 and genetic algorithms. Direct transcription methods has been successfully applied in many fields such as spacecraft trajectory optimization, 17,18 aircraft trajectory optimization 19,20 etc. As stated, in most cases the applied methods cannot provide guarantees on finding the global optimal solution (region of convergence may be very small) and moreover can have severe problems of finding any valid trajectories given the (in)equality constraints imposed on the problem.…”

mentioning

confidence: 99%

Trajectory Optimization Based on Interval Analysis

Weerdt

Kampen

Chu

et al. 2011

AIAA Guidance, Navigation, and Control Conference

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Trajectory optimization has been a large field of research for many years. The drawback is that for non-convex, constrained problems practically all available solvers cannot guarantee that the globally optimal trajectory is found. Interval analysis based solvers however can provide this guarantee. Interval analysis has been applied to trajectory optimization before, but the previously presented methods suffered from major drawbacks which limited their application to small scale problems. In this paper a new interval based method is introduced which incorporates state parameterization to prevent explicit integration. The performance of the proposed method is demonstrated by applying it to a spacecraft formation flying optimization problem. The results are compared with a gradient based solver and it is shown that the interval method is guaranteed to find the global optimal solution. Finally the first steps for another new trajectory optimization method based on interval analysis and direct collocation are presented.

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Flight Testing a Real-Time Direct Collocation Path Planner

Cited by 27 publications

References 15 publications

Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning

Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning

Implementing Conditional Inequality Constraints for Optimal Collision Avoidance

Trajectory Optimization Based on Interval Analysis

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