Robust Trajectory Optimization Research Articles

Multi-Objective Robust Trajectory Design for Powered Descent and Landing

A robust trajectory optimization approach for guidance algorithm gain and target vector selection for powered descent and landing is developed. A genetic algorithm is used to determine optimized guidance algorithm parameters to minimize the impact of initial condition, environment, navigation, and vehicle property uncertainty on flight performance for a given sensor suite. Vehicle state uncertainties are computed efficiently using linear covariance analysis techniques. When implemented in the guidance algorithm, the optimized gains and target vectors shape a trajectory that has more favorable conditions for a given navigation sensor suite, resulting in improved flight performance. As a demonstration of this method, the optimized guidance parameters are found for a multiphase trajectory from powered descent initiation to touchdown for a robotic lunar landing mission. Single-objective optimization results demonstrate a reduction in uncertainty and an improvement in nominal performance. Multi-objective optimization results showing the tradeoff between terminal position uncertainty and total propellant usage are presented for multiple sensor suite compositions. Further, guidance parameters selected using the developed robust trajectory design approach may enable acceptable flight performance with fewer and/or lower-quality sensors. The resulting Pareto fronts present the optimal trade space early in the mission design process to enable informed decision-making.

Robust Trajectory and Resource Optimization for Communication-Assisted UAV SAR Sensing

Robust Trajectory and Resource Optimization for Communication-Assisted UAV SAR Sensing

Robust convex optimization for reentry glide trajectory using polynomial chaos

Aiming at the reentry glide trajectory design of hypersonic vehicles with uncertain parameters, a robust trajectory optimization method is proposed to enhance the anti-interference ability and process reliability. Firstly, a robust trajectory optimization model for re-entry gliding under uncertain conditions is constructed, which is transformed into a deterministic trajectory optimization problem with dimension expansion by using an uncertainty propagation algorithm based on the Gaussian quadrature and non-intrusive polynomial chaos. Then, the convex optimization technology is used to convexity and discretize the problem, and a deterministic trajectory optimization strategy based on the sequential convex optimization algorithm is designed to achieve a fast solution for the high-dimensional deterministic problem. Finally, the hypersonic glide reentry of the American X-33 is chosen as an example for the numerical simulation. The results show that comparing with the traditional deterministic trajectory optimization algorithm, the present method can effectively reduce the impact of random interference on the reentry glide trajectory and improve the reliability and robustness of the trajectory.

Robust trajectory optimization of re-entry flight with prescribed endpoint region via sparse grid ensemble pseudospectral optimal control

This paper introduces a sampling-based computational framework with a pseudospectral transcription, designed to investigate performance-robustness tradeoffs for constrained re-entry flights with a non-Gaussian uncertainty propagation. Ensemble of trajectories which are generated with sparse grids with Conjugate Unscented Transformation have been integrated into the nonlinear programming via a vectorized and parallelized formulation. A cross-range maximization problem is formulated to assess the influences of uncertainties in entry interface conditions and model parametric uncertainties. A comprehensive analysis, facilitated by rapid gradient-based optimization convergence and warm-starting, highlights the significant effects of initial speed uncertainties and drag coefficient on problem feasibility, offering insights into optimal control behavior under different degrees and combinations of uncertainties. Proper scaling of controls and the objective function proves pivotal for achieving convergence. Furthermore, a novel phenomenon called “contact arcs” is discovered, composed of contact points that form an arc at the edge of the path constraint in the constrained ensemble optimal control as a counterpart to the boundary arcs in deterministic optimal control problems. Simulation results show excellent agreement with the derived optimality conditions.

Robust eVTOL trajectory optimization under uncertainties – Challenges and approaches

In the paper at hand an overview of the problem of eVTOL trajectory optimization by means of optimal control methods is given. Especially the question of how to robustly optimize trajectories under uncertainties is discussed. The inherent instability of typical eVTOL configurations in hover and transition represents a significant challenge for robust trajectory optimization. We pinpoint specific arising issues and survey potential solutions.

Analytical Uncertainty Propagation and Robust Trajectory Optimization for Continuous-Thrust Relative Motion

Analytical continuous-thrust uncertainty propagation is derived under the control error and the initial navigation error for the linear relative motion near elliptic orbits. Two continuous-thrust control error models are considered: control-linear error model and thrust-magnitude-direction error model. The analytical uncertainty propagation expression is obtained by using the thrust series expansion with respect to eccentric anomaly. Based on the derived analytical uncertainty propagation, the robust energy-optimum and fuel-optimum orbital rendezvous problems are formulated as nonlinear programming ones. In particular, the robust energy-optimum rendezvous problem under the control-linear error model is converted into solving a one-dimensional equation. Several numerical examples indicate that the derived analytical uncertainty propagation is accurate and that the developed robust trajectory optimization approach is computationally efficient.

Multi-Objective Aircraft Robust Trajectory Optimization Considering Various Predictability Metrics Under Uncertain Wind

Multi-Objective Aircraft Robust Trajectory Optimization Considering Various Predictability Metrics Under Uncertain Wind

Robust Trajectory and Resource Optimization in UAV-Enabled IoT Networks under Probabilistic LoS Channel in Presence of Jammers

This paper studies the anti-jamming problem of unmanned aerial vehicle (UAV)-enabled Internet of Things (IoT) communication networks in the presence of a jammer under the accurate probabilistic line-of-sight (LoS) model. Our goal is to maximize the information collection throughput of the system under the assumption that only the jammer's approximate location is known. To this end, we formulate a throughput maximization problem by optimizing the UAV trajectory, the IoT devices' transmit power, and communication scheduling under the accurate real-time probabilistic LoS channel. However, the proposed optimization problem is non-convex and coupled, and hence intractable to be solved. In order to tackle the problem, a robust iterative algorithm is proposed by leveraging the block coordinate descent (BCD) method, the successive convex approximation (SCA) technology, the difference of convex (D.C) programming approach, and the S-procedure. Extensive simulation results show that our proposed algorithm significantly improves the system throughput while achieving a practical anti-jamming effect compared with the benchmark algorithms.

PCE-Based Robust Trajectory Optimization of Launch Vehicles via Adaptive Sample and Truncation

PCE-Based Robust Trajectory Optimization of Launch Vehicles via Adaptive Sample and Truncation

Uncertain trajectory planning integrating polynomial chaos and convex programming

The present work explores the robust trajectory optimization scheme considering both the initial state disturbance and multiple constraints. An uncertain multi-constraint optimization model has been first established. Due to the existence of the stochastic disturbance, standard numerical trajectory planning algorithms cannot be directly applied to address the considered issue. Hence, based on the intrusive polynomial chaos expansion, we present a deterministic quantification for the stochastic state and constraints, so that the transformed optimization model becomes solvable for standard numerical optimization methods. To obtain the enhanced computational performance, an hp pseudo-spectral sequential convex programming procedure combined with a penalty function and backtracking search is proposed. This is achieved by discretizing and convexifying the nonlinear dynamics/constraints using hp quadrature collocation and successive linearization, respectively, and by adjusting the confidence region manually in the iteration. The simulation of a three-dimensional interception with the specific impact angle is conducted to verify the effectiveness. The simulation results show that the initial solutions are insensitive to the convex optimization, and the control commands generated by the proposed algorithm are effective against the initial state disturbance.

Robust Quantum Optimal Control with Trajectory Optimization

The ability to engineer high-fidelity gates on quantum processors in the presence of systematic errors remains the primary barrier to achieving quantum advantage. Quantum optimal control methods have proven effective in experimentally realizing high-fidelity gates, but they require exquisite calibration to be performant. We apply robust trajectory optimization techniques to suppress gate errors arising from system parameter uncertainty. We propose a derivative-based approach that maintains computational efficiency by using forward-mode differentiation. Additionally, the effect of depolarization on a gate is typically modeled by integrating the Lindblad master equation, which is computationally expensive. We employ a computationally efficient model and utilize time-optimal control to achieve high-fidelity gates in the presence of depolarization. We apply these techniques to a fluxonium qubit and suppress simulated gate errors due to parameter uncertainty below ${10}^{\ensuremath{-}7}$ for static parameter deviations of the order of 1%.

Robust optimization of control command for aerospace vehicles with aerodynamic uncertainty

To reduce the design burden of Aerospace Vehicles (ASVs) control systems, this paper proposes a multi-constrained robust trajectory optimization method, which provides a good front-end input for the control system. Differ from the conventional aircraft, some control performance of ASVs is not only related to the model parameters, but also affected by the flight status. Therefore, the robust optimization method combines this characteristic of ASVs, sets the control performance as one of the optimization objectives, and considers the influence of parameter uncertainty. In this method, the polynomial chaos expansion algorithm is used to transform the trajectory optimization problem with uncertain parameters into the equivalent deterministic robust trajectory optimization problem. Finally, compared with traditional deterministic trajectory optimization methods to illustrate the effectiveness of proposed control optimization method.

Robust Trajectory Planning for Hypersonic Glide Vehicle with Parametric Uncertainties

A hybrid double-loop optimization algorithm combing particle swarm optimization (PSO) and nonintrusive polynomial chaos (NIPC) is proposed for solving the robust trajectory optimization of hypersonic glide vehicle (HGV) under uncertainties. In the outer loop, the PSO method searches globally for the robust optimal control law according to a penalized fitness function that contains the system robustness considerations. In the inner loop, uncertainty propagation of the stochastic system is performed using the NIPC method, to provide statistical moments for the iterative scheme of the PSO method in the outer loop. Only control variables are discretized, and the state constraints are satisfied implicitly through the numerical integration process, which reduces the number of decision variables as well as the huge amount of computation increased by NIPC. In the end, the robust optimal control law is achieved conveniently. Numerical simulations are carried out considering a classical time-optimal trajectory optimization problem of HGV with uncertainties in both initial states and aerodynamic coefficients. The results demonstrate the feasibility and effectiveness of the proposed method.

Robust motion trajectory optimization of overhead cranes based on polynomial chaos expansion

In this paper, we present a polynomial chaos-based framework for the trajectory optimization of an overhead crane system under uncertainty. The main research described in this paper is as follows. First, the deterministic trajectory optimization problem formulation of a two-dimensional overhead crane model is constructed. Based on this basic mathematical formulation, the uncertainty trajectory optimization problem is formed considering the uncertainty of initial state and system parameter. Then, to solve the uncertainty trajectory optimization problem efficiently, a robust trajectory optimization problem formulation is proposed. However, it is difficult to solve the robust trajectory optimization problem directly because it contains stochastic function terms, such as stochastic dynamic equations, constraint functions and objective functions. We consider both the system state and control input as functions of uncertainty and use polynomial chaos expansion to quantify these stochastic functions. An augmented deterministic trajectory optimization problem which can be solved directly is finally obtained. Based on the proposed robust trajectory optimization formation, the motion trajectory optimization of an overhead crane system under two different uncertainty types of is solved. All simulation results are compared with traditional sampling-based Monte Carlo simulations to demonstrate the feasibility and effectiveness of the proposed method.

Robust Trajectory Design for Rendezvous and Proximity Operations with Uncertainties

A robust trajectory optimization approach for rendezvous and proximity operations in perturbed elliptical orbits with uncertainties is proposed. For robust trajectory design, a new discrete-time linear dynamics model describing the relative equations of motion for powered flight in perturbed elliptical orbits is developed. The linear dynamics model is used to formulate a stochastic trajectory optimization problem that takes into account navigation sensor errors, maneuver execution errors, and trajectory and control dispersion. The objective of the stochastic optimization problem is to minimize the sum of the expected maneuver and the maneuver dispersion subject to a constraint on the final state dispersion. A genetic algorithm is used to solve the stochastic trajectory optimization problem, and a series of examples demonstrate that the stochastic maneuver solution can be significantly better than the solution corresponding deterministic trajectory optimization problem. Nonlinear Monte Carlo simulations are used to validate the results.

Robust trajectory optimization using polynomial chaos and convex optimization

The polynomial chaos (PC) theory and direct collocation method have been integrated to solve a lot of robust trajectory optimization problems. However, the computational cost and memory consumption increase significantly with the increase of the dimension of uncertain factors, and the nonlinearity of dynamic equations. To address this issue, a novel robust trajectory optimization procedure combining PC with the convex optimization technique is proposed in this paper. With the proposed procedure, the trajectory optimization can be implemented with high accuracy and efficiency, by taking advantage of the high accuracy of PC in addressing UP for highly nonlinear dynamics and the high efficiency of convex optimization in solving optimal control. The proposed robust trajectory optimization procedure is applied to two examples and compared with the existing method employing PC and the pseudospectral method. The results show that the proposed procedure can obtain highly accurate results similar to the existing method. Moreover, with the increase of random dimension, the optimal trajectory can still be generated very efficiently without significant increase of computational cost. These results demonstrates the effectiveness of the proposed procedure.

Mars entry trajectory planning using robust optimization and uncertainty quantification

Due to the existence of obvious uncertainties within Mars atmospheric entry, design and analysis of the optimal trajectory under uncertainties play a significant role in reducing flight risk and maintaining guidance performance and delivery accuracy. In this paper, using robust optimization strategy and uncertainty quantification technique, we developed an innovative approach for planning the Mars entry trajectory under uncertainties. The main contribution of this work is twofold: one is considering both dynamics parameter uncertainty and initial state uncertainty, and the other is simultaneously focusing on the reliability of constraint satisfaction and insensitivity of performance index towards uncertainties. First, Mars entry trajectory planning problem under uncertainties is formulated as a robust optimization problem. Second, the uncertainty propagation with regard to Mars entry dynamics is derived, and the quantification of objective function and constraints under uncertainties is conducted. Third, the robust trajectory optimization problem is transformed into an equivalent optimal control problem in the expanded higher-dimensional state space by polynomial chaos expansion, and the solution is obtained by the hp-adaptive pseudospectral method. Finally, the effectiveness of the proposed method is verified through two Mars entry optimal trajectory cases. And the obtained optimal trajectories are reliable and evidently robust to uncertainties compared to traditional deterministic optimization and reliability-based optimization.

Robust direct trajectory optimization using approximate invariant funnels

Many critical robotics applications require robustness to disturbances arising from unplanned forces, state uncertainty, and model errors. Motion planning algorithms that explicitly reason about robustness require a coupling of trajectory optimization and feedback design, where the system’s closed-loop response to disturbances is optimized. Due to the often-heavy computational demands of solving such problems, the practical application of robust trajectory optimization in robotics has so far been limited. Motivated by recent work on sums-of-squares verification methods for nonlinear systems, we derive a scalable robust trajectory optimization algorithm that optimizes approximate invariant funnels along the trajectory while planning. For the case of ellipsoidal disturbance sets and LQR feedback controllers, the state and input deviations along a nominal trajectory can be computed locally in closed form, permitting fast evaluation of robust cost and constraint functions and their derivatives. The resulting algorithm is a scalable extension of classical direct transcription that demonstrably improves tracking performance over non-robust formulations while incurring only a modest increase in computational cost. We evaluate the algorithm in several simulated robot control tasks.

Robust trajectory optimization under frictional contact with iterative learning

Optimization is often difficult to apply to robots due to the presence of errors in model parameters, which can cause constraints to be violated during execution on the robot. This paper presents a method to optimize trajectories with large modeling errors using a combination of robust optimization and parameter learning. In particular it considers the context of contact modeling, which is highly susceptible to errors due to uncertain friction estimates, contact point estimates, and sensitivity to noise in actuator effort. A robust time-scaling method is presented that computes a dynamically-feasible, minimum-cost trajectory along a fixed path under frictional contact. The robust optimization model accepts confidence intervals on uncertain parameters, and uses a convex parameterization that computes dynamically-feasible motions in seconds. Optimization is combined with an iterative learning method that uses feedback from execution to learn confidence bounds on modeling parameters. It is applicable to general problems with multiple uncertain parameters that satisfy a monotonicity condition that requires parameters to have conservative and optimistic settings. The method is applied to manipulator performing a “waiter” task, on which an object is moved on a carried tray as quickly as possible, and to a simulated humanoid locomotion task. Experiments demonstrate this method can compensate for large modeling errors within a handful of iterations.

A concurrent optimization approach for energy efficient multiple axis positioning tasks

Automated production systems typically comprise numerous electrical servo drives, many of which conduct positioning motions, e.g. for handling or manipulation tasks. The power electronics of modern multi-axis systems often comprise coupled DC-links, enabling for internal exchange of recuperative brake energy. However, the motion sequences of manipulators are often commanded at maximum dynamics for minimum time motion, neglecting possible optimization potential, e.g. available idle time, leading to inefficient energy management. A robust trajectory optimization approach based on the particle swarm algorithm and well-established path planning methods is presented for the adaption of multi-axis positioning tasks with only two parameters per axis and positioning motion during system run-time. Experimental results prove that, depending on the positioning task and chosen optimization constraints, energy demands are distinctly reduced. The approach is applicable to diverse multi-axis configurations and enables for considerable energy savings without additional hardware invest.