Questions tagged [robotics]
"Robotics is the branch of mechanical engineering, electrical engineering and computer science that deals with the design, construction, operation, and application of robots, as well as computer systems for their control, sensory feedback, and information processing."
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How to calculate a dual $T^*$ given a member $T$ of $\textrm{SE}(3)$?
In reproducing "A Linear-Time Variational Integrator...", I encountered the undefined symbol ${T^k}^*$ in equations 16a and 16b. A professional acquaintance proved to me that ${T^k}^*$ is a ...
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Robotics - Euler Angles from Linear Transformation
In a robotics application (3d Cartesian Space), I need to transform my Point position and orientation in a particular frame to the world frame. The Frame Position and Orientation is known and I was ...
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Algebraic Topology and Robotics
How active is the current research scene on the application of algebraic and differential topology to robotics? I have spent a decent portion of time researching and reading introductory papers, but ...
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Is Koopman operator just like curve fitting?
I am a beginner in Koopman operators，and I want to apply it to the robotics. But I think the Koopman operator approximated by EDMD is more like a fitting tool. Because we always choose some dictionary ...
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Two State Implicit Filter Derivation
I've been reading The "Two-State Implicit Filter – Recursive Estimation for Mobile Robots" by Bloesch. The gist of the paper is it tries to find the balance between a Kalman Filter and a ...
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Infinite-order polynomial convergence
This isn't a question about Taylor series.
A little background: I'm a robotics engineering student looking at polynomial trajectories, specifically using polynomials to define the rate at which the ...
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Pose matrices and robotics 2D movement
I have a robot starting from the origin. It first turns 90 degrees (yaw), then move to (5,10), then it starts to move along its own negative x direction at each step with a translation of 1. Here is ...
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Cotangent lift of the embedding is zero
I am reading the work on variatonal collision integrators from the programmers point of view, since I want to implement it is the software. The work is publicly available here: caltech. I want to ...
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Convexity of minkowski space when two triangles collide
I am working on a Python program to show the collision of two triangles by using Minkowski difference. I am subtracting each point from one triangle from every other point on the other triangle. The ...
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Confused with understanding an equation written with inverse compositional operators
In the paper "Are we ready for Autonomous Driving? The KITTI Vision Benchmark suite" by Lenz and Urtasun (https://www.cvlibs.net/publications/Geiger2012CVPR.pdf) \
The translation error ...
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Riemannian Metric from Hamiltonian?
Suppose I have a robot arm configuration space (c-space) $Q$ and with Lagrangian $L = T - V$ on $TQ$, and I set up the equation of motion
$$\frac{\partial}{\partial t}\left\{\frac{\partial L}{\partial ...
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How to calculate angle of rotation given a vector and a point
sorry if the title seems vague. English is not my first language and I dont know what to search to find the answer to my problem.
I will preface this by explaining the purpose of this question. I have ...
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A single rotation to reach the final pose of a frame
The following question is from Kinematic Analysis of Robot Manipulators by Carl D. Crane, III, Joseph Duffy:
"The transformation that relates the A and B coordinate systems is given as
That is ...
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Find Lattice for 2-Torus with Given Riemannian Metric?
I have a (standard?) 2-torus $T^2$ with a non-standard Riemannian metric on it
\begin{array}{lcr} g(\theta_1,\theta_2) & = & \begin{bmatrix}Izz1 + Izz2 + (L1^2*m1)/4 + L1^2*m2 + (L2^2*m2)/4 + ...
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Why is the energy cost functional mostly defined as $u.u^T$?
In optimal control theory, while minimizing the energy of a say mobile robot, the expression for the cost functional is generally $u.u^T$ where $u$ is the control vector. I searched why the energy ...
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