A near-optimal decoupling principle for nonlinear stochastic systems arising in robotic path planning and control

IEEE Robot. Autom. Lett.

2019

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Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the closed loop feedback gains, that leads to a deterministic perturbation feedback control based solution (T-PFC) to fully observable stochastic optimal control problems, that is nearoptimal to the third order. Extensive numerical simulations validate the theory, revealing a wide range of applicability, coping with medium levels of noise. The performance is compared with Nonlinear Model Predictive Control in several difficult robotic planning and control examples that show near identical performance to NMPC while requiring much lesser computational effort.

Section: Discussion and Comparison Of Methodsmentioning

confidence: 99%

“…T-LQR: T-LQR is implemented using the same nominal cost as T-PFC. However, the cost parameters of the LQR are tuned entirely separately from the nominal cost [11]. ILQG: ILQG is initiated with the same initial guess as the above three methods.…”

Section: Discussion and Comparison Of Methodsmentioning

confidence: 99%

T-PFC: A Trajectory-Optimized Perturbation Feedback Control Approach

Parunandi

IEEE Robot. Autom. Lett.

2019

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“…This problem utilizes the trace of the covariance as the optimization objective and is accompanied by a separate feedback design implemented in the execution of the policy. In a companion paper, we prove the near-optimality of this framework under a small-noise assumption [27], [28].…”

Section: Comparison Of Trajectory Planning Approachesmentioning

confidence: 98%

On the use of the observability gramian for partially observed robotic path planning problems

Rafieisakhaei

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

2017

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Abstract-Optimizing measures of the observability Gramian as a surrogate for the estimation performance may provide irrelevant or misleading trajectories for planning under observation uncertainty. I. INTRODUCTIONThe Observability Gramian (OG) is used to determine the observability of a deterministic linear time-varying system [1]- [3]. For such systems, the properties of the OG have been well-studied [1], [4], [5]. When sensors provide noisy stochastic measurements, the state is only partially observed. The general problem of planning under process and observation uncertainties has been formulated as such a stochastic control problem with noisy observations. The solution of this problem provides an optimal policy via the Hamilton-Jacobi-Bellman equation [6], [7]. However, the computational hurdle for finding a solution to these equations has necessitated the study of a variety of methods to approximate the solution [8]- [11]. One approach has been to maximize the estimation performance by planning for trajectories that can exploit the properties of observation, process and a priori models. We examine the appropriateness or lack thereof of methods based on the OG, and show that they can provide misleading trajectories.Borrowed from deterministic control theory, the OG has been exploited in order to provide more observable trajectories, particularly in trajectory planing problems [12]-[18]. In the special case of a diagonal observation covariance with the same uncertainty level in each direction [1], the Standard Fisher Information Matrix (SFIM) does reduce to the OG. Indeed the usage of the OG in filtering problems has been justified through its connections to the SFIM and its relations to the parameter estimation problem [13], [19]. In fact, tailored to the parameter estimation problem, the SFIM only addresses the amount of information in the measurements alone [1], and neglects both the prior information and process uncertainty. Closely-related approaches are the methods that base their planning on the observation model or the likelihood function [8], [20], and the analysis of this paper can be helpful in providing a better understanding of those problems.

“…The separation-based approach has always been used by Control Engineers in Aerospace Guidance and Robotics problems in a heuristic fashion [3]. However, our recent companion work [10], using the theory of Large Deviations, shows that this separation, results in a near-optimal policy in the small noise case. Moreover, experimental results confirm its validity for moderate noise levels.…”

Section: Stochastic Feedback Control Algorithmmentioning

confidence: 99%

Stochastic feedback control of systems with unknown nonlinear dynamics

Rafieisakhaei

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

2017

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This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an openloop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system, such that under a small noise assumption, the actual states remain close to the optimal trajectory. The trajectory-dependent linearized system is identified using input-output experimental data consisting of the impulse responses of the nominal system. A computational example is given to illustrate the performance of the proposed approach.