[petercorke]

Adds payload_capacity() and removes pay() and paycap(), which it replaces.

payload_capacity(q, tau_m, w, frame="base"): for each configuration (row of q), the multiple of the wrench w that each joint can support without exceeding its torque limit, a matrix of shape (m, n). Each entry is a positive number, inf if the joint has no part in it, or nan if gravity alone is beyond the limit; the minimum over the joints is the capacity and its argmin is the limiting joint. If w is the weight of a 1 kg mass the answer is in kg.

• tau_m is (n,) or (1,n) of maxima (the minimum is the negative), or (2,n) of minima then maxima.
• w is a 6-vector in the base frame (frame="base", default) or the end-effector frame, including the tool (frame="ee"). The Jacobian function is chosen once before the loop. Any other value raises ValueError.
• The motor torque that holds the robot and a payload s·w is gravload − s·Jᵀw, since w is the wrench the payload applies to the robot. This sign is checked against physics that does not use the method (below), and it matters for asymmetric limits.
• Derived from the MATLAB pay and paycap by Bryan Moutrie (@au-phiware), credited in the docstring. The docstring has an example, as code and a .. plot::, of the Puma 560 along a line.

Removed: pay() (it was -J.T @ w, a poor name) and paycap() (its docstring did not match what it returned, Issue #728, and its test was skipped). These are public methods, so this is a breaking change; the replacement is payload_capacity, and the limits layout differs from paycap's (n, 2) with the maximum first. No ! in the title, as agreed for this repository.

Tests (tests/test_payload_capacity.py, 20): the reference is a real mass on the last link, whose gravity load comes from the recursive Newton-Euler dynamics and does not use the method, for the Puma 560 and the Panda with symmetric and asymmetric limits: at 0.999 of the capacity every joint is within its limit, and at 1.01 of it one is not. Also that a mass adds −Jᵀw to the gravity load, the inf and nan cases, a trajectory, a single q, the limit forms, bad shapes and a bad frame, and that a wrench in the end-effector frame equals the same wrench rotated into the base frame.

Changes numerical results or public behaviour: yes, new method; pay and paycap are removed.

Ran: the payload, DHRobot, ERobot, BaseRobot and hasdynamics tests (228 passed, 1 skipped) and mypy (clean, 165 files). Not run: the docs build; the docs/notebooks/payload.ipynb notebook is not part of this PR.

Written by Peter Corke with Claude Code, which fixed a sign error in the first version (the gravity term had the wrong sign relative to the payload term), added frame, and wrote the tests.

🤖 Generated with Claude Code

[codacy-production]

Not up to standards ⛔

🔴 Issues 12 high

Alerts:
⚠ 12 issues (≤ 0 issues of at least minor severity)

Results:
12 new issues

Category	Results
ErrorProne	1 high
Security	11 high

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🟢 Metrics 15 complexity · 0 duplication

Metric	Results
Complexity	15
Duplication	0

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[codecov]

Codecov Report

❌ Patch coverage is 0% with 25 lines in your changes missing coverage. Please review.
✅ Project coverage is 0.00%. Comparing base (aaf0902) to head (7adf729).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/roboticstoolbox/robot/Dynamics.py	0.00%	25 Missing ⚠️

Additional details and impacted files

@@          Coverage Diff          @@
##            main    #881   +/-   ##
=====================================
  Coverage   0.00%   0.00%           
=====================================
  Files        146     146           
  Lines      17200   17164   -36     
=====================================
+ Misses     17200   17164   -36     

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