Towards planning and control of hybrid systems with limit cycle using LQR trees

Rajasekaran, S.; Natarajan, Ramkumar; Taylor, Joshua A.

doi:10.1109/iros.2017.8206409

Cited by 3 publications

(5 citation statements)

References 15 publications

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“…We verify (22) by showing that when Volume(X initial \ X K tree ) = 0, then X K+1 tree \ X K tree has non-zero volume with non-zero probability. First, given T max , let X Tmax initial be the set of all states that can be driven into X goal within T max steps.…”

Section: Proof For Lemma 1 (Cont'd)mentioning

confidence: 96%

“…A popular approach to characterize contact-based dynamics is using piecewise affine (PWA) models. While accurate robot models are fully nonlinear, PWA models are reasonable approximations in the neighborhoods of nominal trajectories/points, just as linear approximations are, with the extra cycle stabilization of hybrid systems in [22]. Transverse dynamics was studied to deal with switching surfaces [23].…”

Section: Introductionmentioning

confidence: 99%

“…These regions are grown backward from the goal in a tree fashion. This technique is called LQR-trees and was originally introduced for smooth continuous-time systems, and also was applied to limit cycle stabilization of hybrid systems in [22]. Transverse dynamics was studied to deal with switching surfaces [23].…”

Section: Introductionmentioning

confidence: 99%

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Sampling-Based Polytopic Trees for Approximate Optimal Control of Piecewise Affine Systems

Sadraddini

Tedrake

2019

2019 International Conference on Robotics and Automation (ICRA)

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Piecewise affine (PWA) systems are widely used to model highly nonlinear behaviors such as contact dynamics in robot locomotion and manipulation. Existing control techniques for PWA systems have computational drawbacks, both in offline design and online implementation. In this paper, we introduce a method to obtain feedback control policies and a corresponding set of admissible initial conditions for discrete-time PWA systems such that all the closed-loop trajectories reach a goal polytope, while a cost function is optimized. The idea is conceptually similar to LQR-trees [1], which consists of 3 steps:(1) open-loop trajectory optimization, (2) feedback control for computation of "funnels" of states around trajectories, and (3) repeating (1) and (2) in a way that the funnels are grown backward from the goal in a tree fashion and fill the state-space as much as possible. We show PWA dynamics can be exploited to combine step (1) and (2) into a single step that is tackled using mixed-integer convex programming, which makes the method suitable for dealing with hard constraints. Illustrative examples on contact-based dynamics are presented.benefit of capturing contact dynamics [8,9]. PWA models are also popular in traffic networks [10] and gene circuits [11].Controlling PWA systems is difficult since the controller has to determine both the temporal order of modes and the inputs applied at each one. Completeness is important -not finding a solution when one exists is undesirable. Given an initial condition and a goal, the (optimal) trajectory that steers the state to the goal while respecting the dynamics and state/control constraints can be obtained using mixed-integer convex programming (MICP). Time is discretized to obtain a finite number of decision variables. Given a discrete-time PWA model and a fixed time horizon (steps required to get into the goal), MICP approaches are sound and complete -they find optimal solutions if they exist. However, they come at a large computational price. Their unreliable computation time, even for obtaining a feasible solution instead of the optimal one, hinders online implementation for robotic tasks with fast dynamics. While there is a great deal of research on improving the runtime of MICP solvers, they are still orders of magnitude too slow for most robot control problems.An alternative is to move much of the computational burden to offline phase so the real-time implantation is a lookup table of simple control laws. However, existing approaches are not efficient even for relatively small systems. (Nondeterministic) finite-state abstractions [12] require state/control discretization, which scales poorly in high dimensions. Synthesizing PWA control laws corresponding to stabilizing piecewise quadratic (PWQ) Lyapunov functions was studied in [13,14]. But the state-control partition producing the control laws was assumed to be the same as those of PWA dynamics, which is very restrictive and the method may fail while other solutions exist [14].Multi-parametric programming [15] for mo...

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Section: Proof For Lemma 1 (Cont'd)mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Sampling-Based Polytopic Trees for Approximate Optimal Control of Piecewise Affine Systems

Sadraddini

Tedrake

2019

2019 International Conference on Robotics and Automation (ICRA)

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“…They also suffer from the narrow passage problem [21], take longer time to converge to a good quality path and have unreliable intermediate path quality [20]. Despite that, samplingbased trajectory optimization methods like LQR trees [9] with very high convergence time have enjoyed success and even been applied to hybrid systems [22]. These methods focus on the conditions for guaranteed execution based on the geometry of the trajectory funnels and the obstacles and even demonstrate it on a spherical quadrotor [23].…”

Section: R Wmentioning

confidence: 99%

“…Alg. (lines [20][21][22]. The low-dimensional free space X 𝐿 \ X 𝑜𝑏𝑠 is discretized to build a graph G 𝐿 to search.…”

Section: B Insat: Interleaving Search and Trajectory Optimizationmentioning

confidence: 99%

Interleaving Graph Search and Trajectory Optimization for Aggressive Quadrotor Flight

Natarajan

Choset

Likhachev

2021

IEEE Robot. Autom. Lett.

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Quadrotors can achieve aggressive flight by tracking complex manuevers and rapidly changing directions. Planning for aggressive flight with trajectory optimization could be incredibly fast, even in higher dimensions, and can account for dynamics of the quadrotor, however, only provides a locally optimal solution. On the other hand, planning with discrete graph search can handle non-convex spaces to guarantee optimality but suffers from exponential complexity with the dimension of search. We introduce a framework for aggressive quadrotor trajectory generation with global reasoning capabilities that combines the best of trajectory optimization and discrete graph search. Specifically, we develop a novel algorithmic framework that interleaves these two methods to complement each other and generate trajectories with provable guarantees on completeness up to discretization. We demonstrate and quantitatively analyze the performance of our algorithm in challenging simulation environments with narrow gaps that create severe attitude constraints and push the dynamic capabilities of the quadrotor. Experiments show the benefits of the proposed algorithmic framework over standalone trajectory optimization and graph search-based planning techniques for aggressive quadrotor flight.

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Tube-based robust reinforcement learning for autonomous maneuver decision for UCAVs

WANG,

ZHENG,

PIAO

et al. 2024

Chinese Journal of Aeronautics

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Towards planning and control of hybrid systems with limit cycle using LQR trees

Cited by 3 publications

References 15 publications

Sampling-Based Polytopic Trees for Approximate Optimal Control of Piecewise Affine Systems

Sampling-Based Polytopic Trees for Approximate Optimal Control of Piecewise Affine Systems

Interleaving Graph Search and Trajectory Optimization for Aggressive Quadrotor Flight

Tube-based robust reinforcement learning for autonomous maneuver decision for UCAVs

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