Trajectory planning for multiple robots in bearing-only target localisation

Leung, Cindy; Huang, Shoudong; Dissanayake, Gamini; Furukawa, Tomonari

doi:10.1109/iros.2005.1545322

Cited by 9 publications

(8 citation statements)

References 15 publications

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“…As a result, it is not surprising that most existing approaches relax the constrains. For instance, full observability is assumed in [9,7], known robot location is assumed in [10], myopic planning is adopted in [8], and discretization of the state and/or actions spaces appears in [11,12,7]. The method proposed in this paper does not rely on any of these assumptions.…”

Section: Introductionmentioning

confidence: 99%

Active Policy Learning for Robot Planning and Exploration under Uncertainty

Martínez-Cantín¹,

Freitas²,

Doucet³

et al. 2007

Robotics: Science and Systems III

117

106

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Abstract-This paper proposes a simulation-based active policy learning algorithm for finite-horizon, partially-observed sequential decision processes. The algorithm is tested in the domain of robot navigation and exploration under uncertainty, where the expected cost is a function of the belief state (filtering distribution). This filtering distribution is in turn nonlinear and subject to discontinuities, which arise because constraints in the robot motion and control models. As a result, the expected cost is non-differentiable and very expensive to simulate. The new algorithm overcomes the first difficulty and reduces the number of simulations as follows. First, it assumes that we have carried out previous evaluations of the expected cost for different corresponding policy parameters. Second, it fits a Gaussian process (GP) regression model to these values, so as to approximate the expected cost as a function of the policy parameters. Third, it uses the GP predicted mean and variance to construct a statistical measure that determines which policy parameters should be used in the next simulation. The process is iterated using the new parameters and the newly gathered expected cost observation. Since the objective is to find the policy parameters that minimize the expected cost, this active learning approach effectively trades-off between exploration (where the GP variance is large) and exploitation (where the GP mean is low). In our experiments, a robot uses the proposed method to plan an optimal path for accomplishing a set of tasks, while maximizing the information about its pose and map estimates. These estimates are obtained with a standard filter for SLAM. Upon gathering new observations, the robot updates the state estimates and is able to replan a new path in the spirit of openloop feedback control.

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Section: Introductionmentioning

confidence: 99%

Active Policy Learning for Robot Planning and Exploration under Uncertainty

Martínez-Cantín¹,

Freitas²,

Doucet³

et al. 2007

Robotics: Science and Systems III

117

106

View full text Add to dashboard Cite

show abstract

“…Maximization of the determinant of the FIM, a determinant lower bound, or a determinant approximation [2,5,6,[14][15][16] effectively minimizes the volume of the uncertainty ellipsoid around the target estimate, but highly eccentric ellipsoid shapes can result [17]. Similar options (sometimes only semantically different) include the trace of the CRLB [18], the trace of the covariance matrix [3], maximization of the smallest FIM eigenvalue [19], minimization of the trace of the inverse of the FIM [20], or minimization of the differential entropy of the posterior target density (equivalent to maximizing the FIM determinant for the Gaussian case) [21].…”

Section: Trajectory Optimization For Bearing-only Trackingmentioning

confidence: 99%

“…Variables not intended to be constrained had values set well out of a realistic range, but not set at infinity to keep gradients meaningful. The potentially active constraints of C are shown in a consolidated notation: (19) The forward component, x, was limited to stay between the approach point, x app = x app_offset + x t , and the wall of the flight facility furthest from it (where the run was started). The approach point itself is only an estimate, changing each epoch, but it does provide some safety buffer until the desired target certainty is reached.…”

Section: Constraintsmentioning

confidence: 99%

Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning

Ross

Cobb²,

Baker³

2014

International Journal of Micro Air Vehicles

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A method is presented to simultaneously solve the optimal control problem and the optimal estimation problem for a bearing-only sensor. For bearing-only systems that require a minimum level of certainty in position relative to a source for mission accomplishment, some amount of maneuver is required to measure range. Traditional methods of trajectory optimization and optimal estimation minimize an information metric. This paper proposes constraining the final value of the information states with known time propagation dynamics relative to a given trajectory which allows for attainment of the required level of information with minimal deviation from a general performance index that can be tailored to a specific vehicle. The proposed method does not suffer from compression of the information metric into a scalar, and provides a route that will attain a particular target estimate quality while maneuvering to a desired relative point or set. An algorithm is created to apply the method in real-time, iteratively estimating target position with an Unscented Kalman Filter and updating the trajectory with an efficient pseudospectral method. Methods and tools required for hardware implementation are presented that apply to any real-time optimal control (RTOC) system. The algorithm is validated with both simulation and flight test, autonomously landing a quadrotor on a wire. INTRODUCTIONBearing-only tracking is a classical navigation problem. Many real-world systems depend on angleonly sensors for target state estimation, such as submarines using only passive sonar, high-speed antiradiation missiles (HARM), robots, and unmanned aerial vehicles (UAVs) using images from an optical sensor. The inability to sense range with each measurement, combined with the inherent nonlinearity of the problem make estimation of a target's location and motion problematic. Moving the sensor orthogonal to the line-of-sight (LOS) generates observability for range estimation, and many researchers have pursued optimal methods for trajectory planning in this context [1][2][3][4][5][6]. Optimal trajectory planning of any sort, however, is notoriously difficult to implement for on-line systems (excepting those simple enough to have a closed-form analytical feedback solution). Notably, recent advances in direct optimization through techniques such as pseudospectral methods (PSM) [7][8][9] have increased the efficiency and stability of obtaining a numeric optimal solution to the point where realtime optimal control (RTOC) of systems with moderate speed dynamics is now possible. This paper proposes a new method of approaching the bearing-only trajectory planning problem that enables simultaneous consideration of both the optimal control problem and a system's prescribed final estimation requirements, overcoming the typical limitations of previous approaches which address each requirement separately. The trajectory planning goal is to provide an optimal trajectory for arrival at a point, or set of points, potentially offset from a relative targe...

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“…One approach is to approximate the belief as a Gaussian and linearize the dynamic and measurement models. These approximations allow trajectories to be evaluated quickly in a model predictive control (MPC) framework [6], [7]. However, these approximations are not always appropriate for nonlinear systems with non-Gaussian beliefs.…”

Section: Introductionmentioning

confidence: 99%

On the Optimality of Ergodic Trajectories for Information Gathering Tasks

Dressel

Kochenderfer

2018

2018 Annual American Control Conference (ACC)

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Recently, ergodic control has been suggested as a means to guide mobile sensors for information gathering tasks. In ergodic control, a mobile sensor follows a trajectory that is ergodic with respect to some information density distribution. A trajectory is ergodic if time spent in a state space region is proportional to the information density of the region. Although ergodic control has shown promising experimental results, there is little understanding of why it works or when it is optimal.In this paper, we study a problem class under which optimal information gathering trajectories are ergodic. This class relies on a submodularity assumption for repeated measurements from the same state. It is assumed that information available in a region decays linearly with time spent there. This assumption informs selection of the horizon used in ergodic trajectory generation. We support our claims with a set of experiments that demonstrate the link between ergodicity, optimal information gathering, and submodularity.

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Trajectory planning for multiple robots in bearing-only target localisation

Cited by 9 publications

References 15 publications

Active Policy Learning for Robot Planning and Exploration under Uncertainty

Active Policy Learning for Robot Planning and Exploration under Uncertainty

Stochastic Real-Time Optimal Control for Bearing-Only Trajectory Planning

On the Optimality of Ergodic Trajectories for Information Gathering Tasks

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