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Related Concept Videos

State Space Representation01:27

State Space Representation

334
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
334
State Space to Transfer Function01:21

State Space to Transfer Function

357
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
357
Transfer Function to State Space01:23

Transfer Function to State Space

465
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
465
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

152
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
152
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

805
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
805
Sampling Plans01:23

Sampling Plans

334
Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Setting Limits on Supersymmetry Using Simplified Models
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The State Space Subdivision Filter for Estimation on SE(2).

Florian Pfaff1, Kailai Li1, Uwe D Hanebeck1

  • 1Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany.

Sensors (Basel, Switzerland)
|September 28, 2021
PubMed
Summary
This summary is machine-generated.

We developed a novel filter for SE(2) domain tracking, improving accuracy and speed. This method enhances object tracking in planar scenarios by efficiently handling correlated position and orientation.

Keywords:
grid filternonlinear filteringperiodic manifoldspecial Euclidean group

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Area of Science:

  • Robotics and Control Systems
  • State Estimation and Filtering Theory
  • Computational Geometry and Manifold Theory

Background:

  • The Special Euclidean group SE(2) is crucial for describing planar object motion, encompassing both position and orientation.
  • The inherent nonlinearity and periodicity of the angle in SE(2) present significant challenges for traditional filtering techniques.
  • Existing methods often struggle with computational complexity or accuracy when dealing with correlated position and orientation states.

Purpose of the Study:

  • To introduce a novel filtering approach designed for the SE(2) domain that addresses its inherent nonlinearities.
  • To develop a filter that efficiently handles correlated position and orientation states in planar tracking scenarios.
  • To demonstrate superior performance compared to existing state-of-the-art filters in terms of accuracy and computational efficiency.

Main Methods:

  • A novel filter is proposed that decomposes the joint probability density into a marginalized density for the periodic angle and a conditional density for the linear position.
  • The state space is discretized along the periodic dimension, with each segment represented by Gaussian parameters and a grid value.
  • This representation allows for the approximation of functions on SE(2) by weighting Gaussians with grid values, effectively interweaving a grid filter with a Kalman filter.

Main Results:

  • The proposed filter demonstrates comparable complexity to grid filters for circular domains while accommodating varying numbers of parameters.
  • In simulated tracking scenarios, the filter significantly outperformed the unscented Kalman filter for manifolds and a dual quaternion-based progressive filter.
  • The filter achieved higher accuracy than a particle filter with one million particles, operating over an order of magnitude faster.

Conclusions:

  • The novel SE(2) filter offers a computationally efficient and highly accurate solution for planar tracking problems with correlated position and orientation.
  • This approach provides a significant advancement over existing filtering techniques, particularly in real-time applications requiring high performance.
  • The method's ability to balance accuracy and speed makes it a valuable tool for robotics and autonomous systems operating in 2D environments.