URSolver

URSolver#

URSolver is a specialized analytical inverse kinematics (IK) solver for the Universal Robots family of 6-DOF manipulators (UR3, UR3e, UR5, UR5e, UR10, UR10e). Unlike numerical solvers, it derives closed-form joint solutions from the robot’s Denavit–Hartenberg (DH) parameters and evaluates them in batch on the GPU through a NVIDIA Warp kernel. This makes it fast, deterministic, and well suited to large-scale batch IK tasks and real-time control where exact solutions are preferred over iterative refinement.

The analytic formulation follows the ur-analytic-ik repository, and the DH parameters for each robot variant are taken from dh_parameters.hh.

DH Parameters#

The UR kinematic chain is described with the standard DH convention:

Joint

theta

d

a

alpha

1

q1

d1

0

+π/2

2

q2

0

a2

0

3

q3

0

a3

0

4

q4

d4

0

+π/2

5

q5

d5

0

-π/2

6

q6

d6

0

0

Setting ur_type in URSolverCfg selects the matching (d1, a2, a3, d4, d5, d6) values and the corresponding URDF asset. The values are reproduced from dh_parameters.hh.

Configuration#

The solver is configured using the URSolverCfg class. Selecting ur_type automatically fills in the DH parameters and the URDF path; the remaining fields default to sensible values and rarely need to be overridden.

import torch
from embodichain.lab.sim.motion.solvers.ur_solver import URSolver, URSolverCfg

cfg = URSolverCfg(
    ur_type="ur10",       # one of: ur3, ur3e, ur5, ur5e, ur10, ur10e
    end_link_name="ee_link",
    root_link_name="base_link",
    # DH parameters are set automatically from ur_type; override only if needed:
    # d1=0.1273, a2=-0.612, a3=-0.5723, d4=0.163941, d5=0.1157, d6=0.0922,
    tcp=[
        [0.0, 1.0, 0.0, 0.0],
        [-1.0, 0.0, 0.0, 0.0],
        [0.0, 0.0, 1.0, 0.12],
        [0.0, 0.0, 0.0, 1.0],
    ],
)

solver = cfg.init_solver(device="cuda")

ur_type selects the robot variant; an unrecognized value raises ValueError at configuration time.

Solution selection#

See shared FK/IK conventions for the common call pattern. UR IK produces eight analytical branches and expands joint-period shifts into 512 candidates per pose. Each candidate must satisfy joint limits and an FK check against the target.

Mode

Validity shape

Joint solution shape

return_all_solutions=False

(B,)

(B, 6); valid candidate closest to qpos_seed.

return_all_solutions=True

(B, 512)

(B, 512, 6); inspect validity before selecting.

 
qpos_seed = torch.tensor(
    [[0.0, -1.5708, 0.0, -1.5708, 0.0, 0.0]], device=solver.device
)
target_pose = solver.get_fk(qpos_seed)
valid, ik_qpos = solver.get_ik(target_pose, qpos_seed=qpos_seed)
valid_all, candidates = solver.get_ik(
    target_pose, qpos_seed=qpos_seed, return_all_solutions=True
)

set_tcp() updates the tool transform used by FK and IK. Use dh_matrix() when inspecting the model’s individual DH transforms.

References#

Contents