A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems

Kirchner, Matthew R.; Hewer, Gary A.; Darbon, Jérôme; Osher, Stanley

doi:10.1109/ccta.2018.8511584

Cited by 12 publications

(17 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A closed-form solution for the optimal control exists in a wide variety of OC problems. Importantly, the PMP can also be applied efficiently when (16) does not admit a closed-form solution but can be computed efficiently.…”

Section: The Pontryagin Maximum Principlementioning

confidence: 99%

A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding

Onken,

Nurbekyan,

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We propose a neural network approach for solving high-dimensional optimal control problems arising in real-time applications. Our approach yields controls in a feedback form and can therefore handle uncertainties such as perturbations to the system's state. We accomplish this by fusing the Pontryagin Maximum Principle (PMP) and Hamilton-Jacobi-Bellman (HJB) approaches and parameterizing the value function with a neural network. We train our neural network model using the objective function of the control problem and penalty terms that enforce the HJB equations. Therefore, our training algorithm does not involve data generated by another algorithm. By training on a distribution of initial states, we ensure the controls' optimality on a large portion of the state-space. Our grid-free approach scales efficiently to dimensions where grids become impractical or infeasible. We demonstrate the effectiveness of our approach on several multi-agent collisionavoidance problems in up to 150 dimensions. Furthermore, we empirically observe that the number of parameters in our approach scales linearly with the dimension of the control problem, thereby mitigating the curse of dimensionality.

show abstract

Section: The Pontryagin Maximum Principlementioning

confidence: 99%

A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding

Onken,

Nurbekyan,

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Penalizers prove helpful in problems similar to (12) [14], [15], [16], [24]. These penalizers improve the training convergence (Sec.…”

Section: B Adding Hjb Penalizersmentioning

confidence: 99%

“…These penalizers improve the training convergence (Sec. III-C) without altering the solution of (12).…”

Section: B Adding Hjb Penalizersmentioning

confidence: 99%

See 1 more Smart Citation

A Neural Network Approach Applied to Multi-Agent Optimal Control

Onken,

Nurbekyan,

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoidance. These problems immediately become highdimensional, even for moderate phase-space dimensions per agent. Our approach fuses the Pontryagin's Maximum Principle and Hamilton-Jacobi-Bellman (HJB) approaches and parameterizes the value function with a neural network. Our approach yields controls in a feedback form for quick calculation and robustness to moderate disturbances to the system.We train our model using the objective function and optimality conditions of the control problem. Therefore, our training algorithm neither involves a data generation phase nor solutions from another algorithm. Our model uses empirically effective HJB penalizers for efficient training. By training on a distribution of initial states, we ensure the controls' optimality is achieved on a large portion of the state-space. Our approach is grid-free and scales efficiently to dimensions where grids become impractical or infeasible. We demonstrate our approach's effectiveness on a 150-dimensional multi-agent problem with obstacles.

show abstract

“…Note that if the goal is a point in R n , then we can represent this by choosing Ω as a ball with arbitrarily small radius. As noted in Kirchner et al (2018a) we solve for the minimum time to reach the set Ω by constructing a newton iteration, starting from an initial guess, t 0 , with…”

Section: Time-optimal Control To a Goal Setmentioning

confidence: 99%

A Level Set Approach to Online Sensing and Trajectory Optimization with Time Delays

Kirchner

2019

IFAC-PapersOnLine

Self Cite

View full text Add to dashboard Cite

Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the operating environment a priori and must continually perform online trajectory optimization in real time after collecting measurements. The sensing and optimization can induce a significant time delay, and must be accounted for when computing the trajectory. This paper utilizes the generalized Hopf formula, which avoids the exponential dimensional scaling typical of other numerical methods for computing solutions to the Hamilton-Jacobi equation. We present as an example a robot that incrementally predicts a communication channel from measurements as it travels. As part of this example, we introduce a seemingly new generalization of a non-parametric formulation of robotic communication channel estimation. New communication measurements are used to improve the channel estimate and online trajectory optimization with time-delay compensation is performed.

show abstract

A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems

Cited by 12 publications

References 27 publications

A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding

A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding

A Neural Network Approach Applied to Multi-Agent Optimal Control

A Level Set Approach to Online Sensing and Trajectory Optimization with Time Delays

Contact Info

Product

Resources

About