feat: differential inverse kinematics for even more speed

[Ipuch]

On examples/inverse_kinematics.py
Time to solve 200 frames with sqpmethod: 0.7363345623016357
Time to solve 200 frames with ipopt: 1.4329211711883545
Time to solve 200 frames with dik: 0.43631577491760254

This PR adds a new method "dik" to InverseKinematics.solve(), as a QP-based alternative to the nonlinear solvers (ipopt, sqpmethod).

Method

Instead of solving the full nonlinear MKO at each frame, dik iteratively solves a linearized Gauss–Newton QP:

min_{ΔQ}  ½ ‖Φ_m(Q) + K_m ΔQ‖²
s.t.       K_h ΔQ = −Φ_h(Q)

where Φ_m are marker defects (with constant Jacobian K_m in natural coordinates) and Φ_h are holonomic constraints — rigid body + joint — with Jacobian K_h. The QP is solved with [proxsuite/proxQP](https://github.com/Simple-Robotics/proxsuite) and iterates until marker objective stagnation and constraint satisfaction (configurable tolerances).

Why add this

• Speed. K_m and the Hessian K_mᵀ K_m + λI are constant and precomputed once outside the frame loop. Each iteration is a warm-started dense QP — much lighter than an IPOPT call. Particularly attractive for batch processing long c3d files.
• Deterministic behavior. Gauss–Newton + equality-constrained QP has predictable per-iteration convergence, easier to tune than a generic NLP.
• Light dependency. Only requires proxsuite (lazy import, clear error if missing).
• Optional step bounds. max_delta_q adds −Δ ≤ ΔQ ≤ Δ box inequalities to stabilize the linearization far from feasible Q.

Usage

ik = InverseKinematics(model, experimental_markers=markers)
Qopt = ik.solve(method="dik")

Defaults: max_iter=100, eps=1e-6, constraint_eps, step_eps, objective_eps=1e-12, regularization=1e-8 (Tikhonov on the Hessian), max_delta_q=inf, proxqp_eps_abs=1e-8, proxqp_max_iter=1000, use_casadi_dik_evaluators=True (holonomic constraints compiled via CasADi Function.expand() — faster than the NumPy path), verbose=False.

Scope / limitations

_validate_dik_problem() restricts dik to the standard marker-based problem. It rejects:

• heatmap data,
• active_direct_frame_constraints=True (segment-determinant inequalities not yet wired in),
• extra objectives added via add_objective (only the default marker least-squares is supported).

Implementation

New private helpers: _validate_dik_problem, _solve_frame_per_frame_dik, _check_proxsuite_available, _setup_dik_evaluator, _dik_marker_defects, _dik_holonomic_constraints, _setup_dik_qp, _solve_dik_qp. The existing _solve_frame_per_frame path is untouched; routing happens in solve(). success_optim is populated per-frame as before.

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This change is 

[Ipuch]

@ANaaim do you want to get a look at it ? :)

[codecov]

Codecov Report

❌ Patch coverage is 84.90566% with 16 lines in your changes missing coverage. Please review.
✅ Project coverage is 85.56%. Comparing base (198adb8) to head (5f69122).
⚠️ Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
bionc/bionc_numpy/inverse_kinematics.py	84.61%	16 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #165      +/-   ##
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+ Coverage   85.07%   85.56%   +0.49%     
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  Files         112      112              
  Lines        6478     6581     +103     
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+ Hits         5511     5631     +120     
+ Misses        967      950      -17     

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