Multiphase mixed-integer optimal control framework for aircraft conflict avoidance

Soler, Manuel; Kamgarpour, Maryam; Tomlin, Claire J.; Staffetti, Ernesto

doi:10.1109/cdc.2012.6426709

Cited by 5 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different gait patterns can be represented by toggling the binary values of Λ i . The time t is discretized using a variable time-step parameterization [32], where each phase has the same number of integration nodes (blue and purple dots) that scale proportionally with respect to the switching timet i .…”

Section: B Minlp Optimal Control Formulationmentioning

confidence: 99%

Automatic Gait Pattern Selection for Legged Robots

Wang

Chatzinikolaidis

Mastalli

et al. 2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

View full text Add to dashboard Cite

An important issue when synthesizing legged locomotion plans is the combinatorial complexity that arises from gait pattern selection. Though it can be defined manually, the gait pattern plays an important role in the feasibility and optimality of a motion with respect to a task. Replacing human intuition with an automatic and efficient approach for gait pattern selection would allow for more autonomous robots, responsive to task and environment changes. To this end, we propose the idea of building a map from task to gait pattern selection for given environment and performance objective. Indeed, we show that for a 2D half-cheetah model and a quadruped robot, a direct mapping between a given task and an optimal gait pattern can be established. We use supervised learning to capture the structure of this map in a form of gait regions. Furthermore, we propose to construct a warmstarting trajectory for each gait region. We empirically show that these warm-starting trajectories improve the convergence speed of our trajectory optimization problem up to 60 times when compared with random initial guesses. Finally, we conduct experimental trials on the ANYmal robot to validate our method.

show abstract

Section: B Minlp Optimal Control Formulationmentioning

confidence: 99%

Automatic Gait Pattern Selection for Legged Robots

Wang

Chatzinikolaidis

Mastalli

et al. 2020

2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

View full text Add to dashboard Cite

show abstract

“…(MIOCP) By discretizing the problem at this stage, one obtains a MINLP [27]. This results in n q binary decision variables for each discretization step and thus, the problem becomes intractable for more than a few number of discrete modes.…”

Section: A Formulation As Miocpmentioning

confidence: 99%

“…We use is the so-called Hermite-Simpson direct collocation method [40]. It has been widely used for solving optimal control problems in aircraft and aerospace applications due to its computational efficiency [43], [27].…”

Section: Formulation As a Nonlinear Programmentioning

confidence: 99%

See 1 more Smart Citation

A Hybrid Optimal Control Approach to Fuel-Efficient Aircraft Conflict Avoidance

Soler

Kamgarpour

Lloret

et al. 2016

IEEE Trans. Intell. Transport. Syst.

Self Cite

View full text Add to dashboard Cite

We formulate fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. The discrete modes of the hybrid system capture the air traffic procedures for conflict resolution, e. g., speed and turn advisories. In order to solve problems of realistic dimensions arising from air traffic sector planning, we formulate a numerically tractable approach to solve the hybrid optimal control problem. The approach is based on introducing binary functions for each mode, relaxing the binary functions and including a penalty term on the relaxation. The transformed and discretized problem is a nonlinear program. We use the approach on a realistic case study with 7 aircraft within an air traffic control sector, in which we find minimum fuel conflict free trajectories.

show abstract

“…Given the switching sequence and times, the third subtask is a regular optimal control problem with a finite number of discontinuities in the system vector field. The necessary condition of optimality in the context of hybrid systems has been derived from Pontryagin's maximum principle (Branicky et al, 1998;Sussmann, 1999;Riedinger et al, 2003) and subsequently, various computational techniques have been developed to solve this problem (Shaikh and Caines, 2007;Soler et al, 2012;Pakniyat and Caines, 2014).…”

Section: Introductionmentioning

confidence: 99%

Sequential Linear Quadratic Optimal Control for Nonlinear Switched Systems

et al. 2017

Self Cite

View full text Add to dashboard Cite

In this contribution, we introduce an efficient method for solving the optimal control problem for an unconstrained nonlinear switched system with an arbitrary cost function. We assume that the sequence of the switching modes are given but the switching time in between consecutive modes remains to be optimized. The proposed method uses a two-stage approach as introduced by Xu and Antsaklis (2004) where the original optimal control problem is transcribed into an equivalent problem parametrized by the switching times and the optimal control policy is obtained based on the solution of a two-point boundary value differential equation. The main contribution of this paper is to use a Sequential Linear Quadratic approach to synthesize the optimal controller instead of solving a boundary value problem. The proposed method is numerically more efficient and scales very well to the high dimensional problems. In order to evaluate its performance, we use two numerical examples as benchmarks to compare against the baseline algorithm. In the third numerical example, we apply the proposed algorithm to the Center of Mass control problem in a quadruped robot locomotion task.

show abstract

Multiphase mixed-integer optimal control framework for aircraft conflict avoidance

Cited by 5 publications

References 25 publications

Automatic Gait Pattern Selection for Legged Robots

Automatic Gait Pattern Selection for Legged Robots

A Hybrid Optimal Control Approach to Fuel-Efficient Aircraft Conflict Avoidance

Sequential Linear Quadratic Optimal Control for Nonlinear Switched Systems

Contact Info

Product

Resources

About