Feedback motion planning under non-Gaussian uncertainty and non-convex state constraints

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

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Motion Planning for Active Data Association and Localization in Non-Gaussian Belief Spaces

Springer Proceedings in Advanced Robotics - Algorithmic Foundations of Robotics XII ◽

10.1007/978-3-030-43089-4_19 ◽

2020 ◽

pp. 288-303

Author(s):

Saurav Agarwal ◽

Amirhossein Tamjidi ◽

Suman Chakravorty

Keyword(s):

Motion Planning ◽

Data Association ◽

Active Data ◽

Non Gaussian

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Stochastic Optimal Motion Planning for the Attitude Kinematics of a Rigid Body With Non-Gaussian Uncertainties

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4027950 ◽

2014 ◽

Vol 137 (3) ◽

Cited By ~ 1

Author(s):

Taeyoung Lee

Keyword(s):

Rigid Body ◽

Motion Planning ◽

Uncertainty Propagation ◽

Planck Equation ◽

Uncertain Environments ◽

Stochastic Motion ◽

Stochastic Optimal Control Problem ◽

Optimal Motion Planning ◽

Non Gaussian ◽

Global Uncertainty

This paper investigates global uncertainty propagation and stochastic motion planning for the attitude kinematics of a rigid body. The Fokker–Planck equation on the special orthogonal group is numerically solved via noncommutative harmonic analysis to propagate a probability density function along flows of the attitude kinematics. Based on this, a stochastic optimal control problem is formulated to rotate a rigid body while avoiding obstacles within uncertain environments in an optimal fashion. The proposed intrinsic, geometric formulation does not require the common assumption that uncertainties are Gaussian or localized. It can be also applied to complex rotational maneuvers of a rigid body without singularities in a unified way. The desirable properties are illustrated by numerical examples.

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A motion planning method for unmanned surface vehicle in restricted waters

Proceedings of the Institution of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment ◽

10.1177/1475090219898566 ◽

2020 ◽

Vol 234 (2) ◽

pp. 332-345

Author(s):

Shangding Gu ◽

Chunhui Zhou ◽

Yuanqiao Wen ◽

Xi Zhong ◽

Man Zhu ◽

...

Keyword(s):

Motion Planning ◽

Shortest Path ◽

State Constraints ◽

Planning Method ◽

A Algorithm ◽

Unmanned Surface Vehicle ◽

Motion State ◽

Vehicle Motion ◽

Three Stages ◽

Vehicle Trajectory

The maneuvering characteristics of the unmanned surface vehicle itself are very important to motion planning due to the limited water scale area. If the size, motion state, and maneuvering characteristics of the unmanned surface vehicle are not considered, the shortest path obtained is actually not feasible in the restricted waters. In this article, the widely used A* algorithm is improved by accounting for the maneuvering characteristics of the unmanned surface vehicle, named as the Label-A* Algorithm, which is further employed to fix the problem related to the motion planning for the unmanned surface vehicle in restricted waters. The solution to the motion planning mainly contains three stages. First, the unmanned surface vehicle trajectory unit library is established based on its maneuvering characteristics; second, an improved label-A* Algorithm is constructed, and the unmanned surface vehicle motion planning method is proposed with the trajectory unit, which is suitable for the restricted waters; Finally, numerical simulations and filed tests are designed to verify the formulated model and proposed algorithm. The motion planning method can simultaneously meet the state constraints, maneuvering characteristics constraints, and water scale constraints of unmanned surface vehicle.

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A New Constrained State Estimation Method Based on Unscented H∞ Filtering

Applied Sciences ◽

10.3390/app10238484 ◽

2020 ◽

Vol 10 (23) ◽

pp. 8484

Author(s):

Yuanyuan Liu ◽

Yaqiong Fu ◽

Huipin Lin ◽

Jingbiao Liu ◽

Mingyu Gao ◽

...

Keyword(s):

Kalman Filter ◽

State Estimation ◽

State Constraints ◽

Unscented Kalman Filter ◽

Estimation Method ◽

The State ◽

Soc Estimation ◽

Non Gaussian ◽

Physical Laws ◽

Broad Overview

The unscented Kalman filter (UKF) is widely used in many fields. When the unscented Kalman filter is combined with the H∞ filter (HF), the obtained unscented H∞ filtering (UHF) is very suitable for state estimation of nonlinear non-Gaussian systems. However, the application of state estimation is often limited by physical laws and mathematical models on some occasions. The standard unscented H∞ filtering always performs poorly under this situation. To solve this problem, this paper improves the UHF algorithm based on state constraints and studies the UHF algorithm based on the projection method. The standard UHF sigma points that violate the state constraints are projected onto the constraint boundary. Firstly, the paper gives a broad overview of H∞ filtering and unscented H∞ filtering, then addresses the issue of how to add constraints using the UHF approach, and finally, the new method is tested and evaluated by the gas-phase reversible reaction and the State of Charge (SOC) estimation examples. Simulation results show the validity and feasibility of the state-constrained UHF algorithm.

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Dual objective motion planning subject to state constraints

Robotica ◽

10.1017/s026357471500106x ◽

2015 ◽

Vol 35 (5) ◽

pp. 1157-1175

Author(s):

Nader Sadegh

Keyword(s):

Computational Complexity ◽

Motion Planning ◽

Autonomous Vehicles ◽

Optimal Trajectory ◽

Degrees Of Freedom ◽

State Constraints ◽

Time Algorithm ◽

Planning Approach ◽

Secondary Objective ◽

Three Degrees Of Freedom

SUMMARYThis paper presents a novel motion planning approach inspired by the Dynamic Programming (DP) applicable to multi degree of freedom robots (mobile or stationary) and autonomous vehicles. The proposed discrete–time algorithm enables a robot to reach its destination through an arbitrary obstacle field in the fewest number of time steps possible while minimizing a secondary objective function. Furthermore, the resulting optimal trajectory is guaranteed to be globally optimal while incorporating state constraints such as velocity, acceleration, and jerk limits. The optimal trajectories furnished by the algorithm may be further updated in real time to accommodate changes in the obstacle field and/or cost function. The algorithm is proven to terminate in a finite number of steps without its computational complexity increasing with the type or number of obstacles. The effectiveness of the global and replanning algorithms are demonstrated on a planar mobile robot with three degrees of freedom subject to velocity and acceleration limits. The computational complexity of the two algorithms are also compared to that of an A*–type search.

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