Add aba function

[Giulero]

This PR introduces the implementation of the Articulated Body Algorithm.

Copilot summary

Articulated-Body Algorithm (ABA) Implementation

• Added a complete implementation of the ABA for floating-base forward dynamics in src/adam/core/rbd_algorithms.py, supporting batched inputs, external wrenches, and both velocity representations. This enables efficient computation of joint and base accelerations for robots.
• Added corresponding ABA wrapper methods to the CasADi (src/adam/casadi/computations.py) and JAX (src/adam/jax/computations.py) computation classes, along with symbolic function support for CasADi. [1] [2]

Matrix Algebra API Extensions

• Introduced new matrix algebra methods (inv, solve, mtimes, expand_dims) to the spatial math abstract base class (src/adam/core/spatial_math.py) and implemented them for Array API, CasADi, and JAX backends. This provides a uniform interface for matrix inversion, solving linear systems, multiplication, and dimension expansion. [1] [2] [3] [4]

Minor Code and Docstring Cleanups

• Standardized docstring formatting (e.g., replacing curly apostrophes) and clarified comments in several places for consistency and readability. [1] [2]
• Minor logic simplification in the Jacobian computation and removal of unnecessary blank lines. [1] [2]

Small API Consistency Fixes

• Fixed a parameter naming inconsistency in the spatial math vxs method, changing c to s for clarity and consistency across the codebase. [1] [2]

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References:
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

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📚 Documentation preview 📚: https://adam-docs--138.org.readthedocs.build/en/138/

[Copilot]

Pull Request Overview

This PR implements the Articulated Body Algorithm (ABA) for efficient floating-base forward dynamics computation in the ADAM robotics library, adding complete support across all backends with corresponding test coverage.

• Added comprehensive ABA implementation in the core RBD algorithms with batched input support and external wrench handling
• Extended spatial math APIs with new matrix operations (inv, solve, mtimes, expand_dims) required for ABA across all backends
• Added extensive test coverage for ABA functionality across NumPy, JAX, PyTorch, and CasADi backends

Reviewed Changes

Copilot reviewed 17 out of 17 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
src/adam/core/rbd_algorithms.py	Core ABA implementation with floating-base dynamics, external wrenches support, and batch processing
src/adam/core/spatial_math.py	Added abstract methods for inv, solve, mtimes operations and fixed parameter naming in vxs method
src/adam/core/array_api_math.py	Implemented new matrix operations for Array API backend
src/adam/casadi/casadi_like.py	Added CasADi-specific implementations of new matrix operations
src/adam/casadi/computations.py	Added ABA wrapper method and symbolic function support for CasADi
src/adam/jax/jax_like.py	JAX-specific solve implementation handling batched operations correctly
src/adam/jax/computations.py	Added JAX ABA wrapper method
src/adam/pytorch/torch_like.py	PyTorch-specific solve override to avoid array_api_compat issues
src/adam/pytorch/computations.py	Added PyTorch ABA wrapper method
src/adam/pytorch/computation_batch.py	Added batched PyTorch ABA wrapper method
src/adam/numpy/computations.py	Added NumPy ABA wrapper method
tests/*.py	Comprehensive test coverage for ABA across all backends with validation against equations of motion

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[Copilot]

Pull Request Overview

Copilot reviewed 18 out of 18 changed files in this pull request and generated 2 comments.

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[Copilot]

Pull Request Overview

Copilot reviewed 18 out of 18 changed files in this pull request and generated no new comments.

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[xela-95]

Thanks @Giulero ! It looks good to me :)

[Giulero]

Tests are passing! Merging!
Thanks :)