T-LQG: Closed-loop belief space planning via trajectory-optimized LQG

Rafieisakhaei, Mohammadhussein; Chakravorty, Suman

doi:10.1109/icra.2017.7989080

Cited by 19 publications

(21 citation statements)

References 14 publications

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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: 97%

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

Rafieisakhaei

Chakravorty

2017

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

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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.

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Section: Comparison Of Trajectory Planning Approachesmentioning

confidence: 97%

“…Problem 3: T-LQG Planning Problem [27] Solve for the optimal linearization trajectory of the LQG policy:…”

Section: Comparison Of Trajectory Planning Approachesmentioning

confidence: 99%

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

Rafieisakhaei

Chakravorty

2017

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

Self Cite

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“…However, ignoring the effects of stochastic future observations can degrade the performance (van den Berg et al, 2012). Other methods (Rafieisakhaei et al, 2017; van den Berg et al, 2012) that do not rely on the MLO assumption are advantageous in that regard. In particular, belief iterative linear quadratic Gaussian (iLQG) (van den Berg et al, 2012) performs iterative local optimization in a Gaussian belief space by quadratically approximating the value function and linearizing the dynamics to obtain a time-varying affine feedback policy.…”

Section: Introductionmentioning

confidence: 99%

SACBP: Belief space planning for continuous-time dynamical systems via stochastic sequential action control

Nishimura

Schwager

2021

The International Journal of Robotics Research

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We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and extends sequential action control to stochastic dynamics. The resulting algorithm, which we name SACBP, does not require discretization of spaces or time and synthesizes control signals in near real-time. SACBP is an anytime algorithm that can handle general parametric Bayesian filters under certain assumptions. We demonstrate the effectiveness of our approach in an active sensing scenario and a model-based Bayesian reinforcement learning problem. In these challenging problems, we show that the algorithm significantly outperforms other existing solution techniques including approximate dynamic programming and local trajectory optimization.

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“…In particular POMDPs are notorious for their computational complexity that may prohibit their application for navigation in complex or uncertain environments in high dimensional state spaces. In [2] a more scalable LQG variant is proposed and applied to environments with discontinuous sensing regions. An approximate solution to POMDPs is given in [3] but with the use of considerable pre-processing.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Time Trajectory Planning Under Intermittent Measurements

Penin

Giordano

Chaumette

2019

IEEE Robot. Autom. Lett.

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This paper focuses on finding robust paths for a robotic system by taking into account the state uncertainty and the probability of collision. We are interested in dealing with intermittent exteroceptive measurements (e.g., collected from vision). We assume that these cues provide reliable measurements that will update a state estimation algorithm wherever they are available. The planner has to manage two tasks: reaching the goal in a minimum time and collecting sufficient measurements to reach the goal state with a given confidence level. We present a robust perception-aware bi-directional A* planner for differentially flat systems such as a unicycle and a quadrotor UAV and use a derivative-free Kalman filter to approximate the belief dynamics in the flat space. We also propose an efficient way of ensuring continuity and feasibility by exploiting the convex-hull property of B-spline curves.

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T-LQG: Closed-loop belief space planning via trajectory-optimized LQG

Cited by 19 publications

References 14 publications

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

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

SACBP: Belief space planning for continuous-time dynamical systems via stochastic sequential action control

Minimum-Time Trajectory Planning Under Intermittent Measurements

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