RobotArmNode#

Module: mime.nodes.actuation.robot_arm Stability: experimental Algorithm ID: MIME-NODE-102 Version: 1.0.0 Verification Mode: Mode 2 (Independent)

Summary#

URDF-driven articulated rigid-body manipulator. Kinematic and inertial structure is parsed once at construction from a URDF file; joint-space dynamics are integrated each step with semi-implicit Euler, using mass matrix from CRBA, nonlinear bias from RNEA, and per-link external wrenches mapped via Jacobian transpose. v1 is fully rigid (no flexibility, no contact, no cogging).

Governing Equations#

$$ M(q),\ddot q + c(q,\dot q) + g(q) ;=; \tau_{\mathrm{eff}} + \sum_i J_i^{!\top},F^{\mathrm{ext}}_i $$

with $$ \tau_{\mathrm{eff}} = \tau_{\mathrm{cmd}} - f \cdot \dot q, \qquad J_i = J_{\mathrm{geom}}(q, i) \in \mathbb{R}^{6\times N}. $$

Integration:

$$ \dot q_{n+1} = \dot q_n + \ddot q,\Delta t, \qquad q_{n+1} = q_n + \dot q_{n+1},\Delta t, \qquad q_{n+1} \leftarrow \mathrm{clip}(q_{n+1};,q_{\mathrm{lo}},q_{\mathrm{hi}}). $$

Discretization#

Semi-implicit (symplectic) Euler with explicit forces. The mass matrix $M(q)$ is built by a vectorised CRBA pass using ancestor masking; the nonlinear bias $c(q,\dot q) + g(q)$ is computed by a single RNEA pass. Each per-link 6-DOF external wrench is multiplied by the transpose of that link’s geometric Jacobian (linear-then-angular ordering). Joint limits are enforced by hard clipping after the position update.

Implementation Mapping#

Equation Term

Implementation

Notes

$M(q)$ — joint-space mass matrix

mime.control.kinematics.crba.mass_matrix

CRBA, ancestor mask

$c(q,\dot q)+g(q)$ — nonlinear bias

mime.control.kinematics.rnea.nonlinear_bias

RNEA single pass

$J_i$ — geometric Jacobian for link $i$

mime.control.kinematics.fk.frame_jacobian

linear-angular ordering

$\sum_i J_i^{!\top}F^{\mathrm{ext}}_i$

mime.nodes.actuation.robot_arm._wrench_to_joint_torques

static-N unrolled loop

$\ddot q = M^{-1}(\tau_{\mathrm{eff}} + \tau_{\mathrm{ext}} - \mathrm{bias})$

mime.nodes.actuation.robot_arm.RobotArmNode.update

jnp.linalg.solve

Semi-implicit Euler $q,\dot q$ update

mime.nodes.actuation.robot_arm.RobotArmNode.update

clip to limits

Forward kinematics — link / EE poses

mime.control.kinematics.fk.link_world_poses

URDF link-COM frames

Pose composition base ⊕ link ⊕ tool

mime.nodes.actuation.robot_arm.RobotArmNode.compute_boundary_fluxes

scalar-first quat

Assumptions and Simplifications#

  1. Rigid joints — no flexibility, backlash, or compliant stops.

  2. Linear viscous joint friction $\tau_f = f,\dot q$. Coulomb friction not modelled.

  3. Fixed base — base_pose_world is held constant by the caller.

  4. Gravity is treated as a uniform inertial field in world coordinates.

  5. External wrenches are expressed in world coordinates and applied at each link’s inertial origin (the URDF <inertial><origin>).

  6. URDF fixed joints are merged at parse time — caller cannot re-introduce a fixed joint at runtime.

Validated Physical Regimes#

Parameter

Verified Range

Notes

num_joints

1 – 10

Tested on 3-link planar fixture; algorithm scales further

Timestep

$10^{-4}$ – $10^{-2}$ s

Stable for revolute manipulators with reasonable inertias

Known Limitations and Failure Modes#

  1. No contact / collision detection: links can pass through each other or through the world without any reaction force.

  2. Joint limit clipping is hard — $\dot q$ is not zeroed at the limit, so the arm can integrate against the wall and produce large reaction spikes if energy is supplied.

  3. Single solve per step — no fixed-point iteration with downstream nodes beyond what GraphManager’s coupling-group machinery provides.

  4. Cogging torque, rotor imbalance, and motor current draw belong to MotorNode (the magnet-rotor stage at the EE), not this node. The per-axis arm motors are abstracted into joint-space torques / friction.

Stability Conditions#

Empirical: dt < 1e-2 s for typical revolute manipulators; tighter at high stiffness. The semi-implicit scheme is symplectic, so energy drift on conservative systems is bounded over long horizons.

State Variables#

Field

Shape

Units

Description

joint_angles

(N,)

rad

$q$

joint_velocities

(N,)

rad/s

$\dot q$

Parameters#

Parameter

Type

Default

Units

Description

urdf_path

str

— (required)

—

URDF file path

end_effector_link_name

str

— (required)

—

URDF link name to expose as EE

end_effector_offset_in_link

tuple[7]

identity

m, quat

tool-tip offset in EE-link frame

base_pose_world

tuple[7]

identity

m, quat

world pose of root link

joint_friction_n_m_s

tuple[N] or None

URDF damping

N·m·s/rad

per-joint viscous friction

gravity_world

tuple[3]

(0,0,-9.80665)

m/s²

world-frame gravity

joint_limit_override

tuple[(N,2)] or None

URDF limits

rad

(lower, upper) per joint

Boundary Inputs#

Field

Shape

Default

Coupling Type

Description

commanded_joint_torques

(N,)

zeros

additive

$\tau_{\mathrm{cmd}}$

external_wrenches_per_link

(N, 6)

zeros

additive

per-link world-frame wrench [F_lin; F_ang]

Boundary Fluxes (outputs)#

Field

Shape

Units

Description

end_effector_pose_world

(7,)

m, quat

tool-tip pose, scalar-first quat

link_poses_world

(N, 7)

m, quat

URDF link-COM poses

joint_angles

(N,)

rad

$q$

joint_velocities

(N,)

rad/s

$\dot q$

joint_torques_actual

(N,)

N·m

$\tau_{\mathrm{cmd}} - f\dot q + J^\top F_{\mathrm{ext}}$

MIME-Specific Sections#

Anatomical Operating Context#

Not applicable — RobotArmNode is an external apparatus operating in the lab frame, not in any anatomical compartment. Its base pose is positioned outside the patient.

Clinical Relevance#

The arm carries the magnet-rotor + permanent-magnet stage at its end-effector. Its kinematic precision and stiffness directly determine the achievable accuracy of microrobot actuation: lateral drift of the EE relative to the microrobot’s vessel translates into the misalignment-induced wobble / step-out reduction effects analysed in the actuation-decomposition plan. This node is not in patient contact and makes no clinical claims.

Mode 2 Independent Verification#

All verification is independent (no MADDENING upstream wraps a multibody arm). Evidence: MIME-VER-120 / 121 / 122 / 123 / 124.

References#

  • [@Featherstone2008] Featherstone, R. (2008). Rigid Body Dynamics Algorithms. Springer. — CRBA, RNEA, spatial-vector formulations.

  • [@Sciavicco2000] Sciavicco, L. & Siciliano, B. (2000). Modelling and Control of Robot Manipulators. Springer. — Jacobian-transpose wrench mapping; PD with gravity compensation.

  • [@Annin2024AR4] Annin, C. (2024). AR4 Open-Source 6-DOF Robot Arm. — URDF and STL meshes for the bundled default-arm experiment under MICROROBOTICA/experiments/ar4_helical_drive/.

Verification Evidence#

  • tests/verification/test_robot_arm.py

  • docs/validation/benchmark_reports/mime_ver_120_robot_arm_fk.md

  • docs/validation/benchmark_reports/mime_ver_121_robot_arm_mass_matrix.md

  • docs/validation/benchmark_reports/mime_ver_122_robot_arm_free_fall.md

  • docs/validation/benchmark_reports/mime_ver_123_robot_arm_gravity_hold.md

  • docs/validation/benchmark_reports/mime_ver_124_robot_arm_pd_tracking.md

Changelog#

Version

Date

Change

1.0.0

2026-04-30

Initial implementation. URDF parsing via mime.control.kinematics.urdf.parse_urdf. CRBA + RNEA pure-JAX path. Five Mode-2 verification benchmarks.