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Twist as displacement vs velocity: document both, and decide Twist3 * SpatialVelocity and Twist/SpatialVelocity conversion

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文档
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python
领域
api, documentation

调研方向

Start with the Twist2/Twist3 class docstrings and the module note in spatialvector.py, which covers SpatialVelocity and the translational-first layout. Read SpatialVector.__rmul__ to see how Twist3 * SpatialVector currently computes Ad(exp(S)) · v. The first step is a maintainer decision on the two open questions, since the docs change depends on it. Done means the docstrings state both readings, mark which properties are scale-invariant, and link to SpatialVelocity.

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描述

documentation enhancement

Background

Twist2 and Twist3 hold an element of se(2) / se(3) as a vector [v, ω]. In robotics a "twist" is used in two ways that share the same vector, the same layout and the same algebra, but have different physical meaning:

Displacement (screw) Velocity
What S is the log of a pose; often a unit screw axis times a magnitude an instantaneous rate, with units m/s and rad/s
Pose from it exp(S), or exp(S * theta) for a unit S exp(S * dt) over a time dt
Used in RVC (§2.3.2.3), Modern Robotics (Lynch & Park), product-of-exponentials kinematics ROS geometry_msgs/Twist, differential kinematics

The class is currently written for the first reading (unit(), pitch, line(), exp(theta)), but nothing in the docs says so, and users arriving from ROS reasonably expect the second.

SpatialVelocity already exists in spatialvector.py as part of the Featherstone family (velocity, acceleration, force, momentum). It uses the same translational-first layout as Twist3 (see the module note), and it is the right home for the velocity reading, because force and momentum are dual to motion and transform with the coadjoint (see #207).

What is not proposed

  • Renaming Twist2/Twist3, or adding a second twist-like class. The algebra is identical, so that would duplicate it, and Twist is the term used in RVC and RTB.

Why it matters in practice

Most operations are the same under both readings. The ones that describe the screw axis are invariant to scaling the twist, so they hold for both: pitch, line() (Plücker coordinates scale but the line does not) and pole. pole was the one place that silently assumed |ω| = 1, which #249 fixes. The ones that depend on magnitude (theta, exp(S * k)) are an angle in one reading and a rate in the other.

The interpretation also leaks into behaviour in one place, which is the first question below.

Proposed

A docs-only change so the class docstrings describe both usages, say which properties are scale-invariant, and point to SpatialVelocity.

Open questions

1. What should Twist3 * SpatialVelocity (and the other SpatialVector types) mean?

Since #210, it computes Ad(exp(S)) · v via SpatialVector.__rmul__. That is the displacement reading: the twist acts as the pose exp(S), the same as SE3 * v. Under the velocity reading the natural action of one velocity on another is the Lie bracket ad(S) · v, which SpatialVelocity @ already provides, and exp(S) would carry an implicit dt = 1.

Options:

  • (a) Keep it, and document * as the finite-displacement action.
  • (b) Keep it, and also make the bracket route easy to find from Twist3.
  • (c) Make * require an SE3 and have the user write S.SE3() * v, so the choice is explicit.

2. Should there be explicit conversion between Twist3 and SpatialVelocity (and Twist2 where it applies)?

The layouts match, so it is trivial, and it would make the relationship discoverable. Things to decide: constructors (SpatialVelocity(twist) / Twist3(velocity)) versus named methods, and whether a conversion should say anything about dt or the frame, since SpatialVelocity here carries no frame tag.

Related

  • #207, #210: spatial vector transforms and Twist3 * SpatialVector
  • #249: pole made invariant to scaling the twist
  • Featherstone, Rigid Body Dynamics Algorithms; Murray, Li & Sastry, A Mathematical Introduction to Robotic Manipulation
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