Exploring PolicyIK: High-Precision I in Robot Kinematics

• Inverse Kinematics (IK) is a mapping from a desired end-effector pose to a set of joint configurations in a robot's arm. This involves forecasting compensations for drag and friction forces to optimize the robot’s movement.
• PolicyIK is a closed-loop pose regulation solution that repeatedly updates joint-position references, achieving mean final-second errors under 1 mm and 0.2° with precise torque distribution.
• It excels with real robots, showing 95.7% simulated pick-and-place success, while also noting that further adaptation mechanisms are needed at different physical constraints performing math computations.

PolicyIK is a goal-conditioned reinforcement-learning policy for high-precision inverse kinematics (IK) in robot arms. It treats IK as closed-loop pose regulation rather than as a one-time solution of $\operatorname{FK}(q)=T_g$: the policy repeatedly updates a joint-position reference from pose feedback while preserving the reference offset required by the physical execution controller. Its design combines accumulated reference updates, reference-state observation, two-scale pose-error features, error-dependent action gains, progress and dwell rewards, and goal-conditioned training. In simulation on a fixed-base 7-DoF OpenArm, PolicyIK achieves mean final-second errors within $1\,\mathrm{mm}$ and $0.2^\circ$ on $93.5\%$ of held-out tasks in a single attempt and $98.9\%$ with a deployment protocol. It also improves reaching and holding success on physical robot experiments and executes the end-effector commands of a $\pi_{0.5}$ vision-language-action policy with $95.7\%$ simulated pick-and-place success (Liu et al., 3 Nov 2026).

1. Problem formulation and motivation

Inverse kinematics maps a desired end-effector pose to a joint configuration or joint motion. For a robot with joint state $q\in\mathbb{R}^{7}$, forward kinematics is represented as

$T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$

where $R(q)$ is orientation and $1\,\mathrm{mm}$0 is position. Given a target pose $1\,\mathrm{mm}$1, conventional IK seeks a configuration $1\,\mathrm{mm}$2 satisfying the target approximately, often through analytical solutions, Jacobian-based differential IK, damped least squares (DLS), constrained quadratic programming (QP), or model-predictive control (MPC).

The paper distinguishes numerical kinematic accuracy from physical execution accuracy. A position-controlled arm may not settle at the mathematically desired joint configuration because of gravity, finite controller gains, effort limits, joint constraints, and unmodeled dynamics. In an approximate static equilibrium for an uncompensated proportional controller,

$1\,\mathrm{mm}$3

where $1\,\mathrm{mm}$4 is the commanded joint reference, $1\,\mathrm{mm}$5 is the realized joint configuration, and $1\,\mathrm{mm}$6 is the gravity torque. Consequently, the reference needed for accurate physical holding may differ from the nominal IK solution.

Redundancy and singularities further complicate the problem. Multiple joint configurations can realize the same end-effector pose, while near a singularity a small Cartesian correction can require a large joint displacement. Classical methods must balance precision, speed, joint-limit avoidance, damping, secondary objectives, and controller-specific tuning. PolicyIK instead learns a closed-loop mapping that incorporates the robot’s dynamics and the behavior of the downstream joint-position controller.

The evaluation uses position and orientation errors

$1\,\mathrm{mm}$7

and

$1\,\mathrm{mm}$8

The strict terminal criterion is

$1\,\mathrm{mm}$9

In simulation, success is determined by the mean errors over the final $0.2^\circ$0 control steps, corresponding to one second at a $0.2^\circ$1 Hz policy rate. A stronger containment metric requires every sample in that final window to remain within both tolerances.

2. Accumulated reference control

The defining architectural choice in PolicyIK is that the policy outputs increments to an accumulated joint-position reference rather than absolute joint targets or corrections directly relative to the measured joints. The reference evolves according to

$0.2^\circ$2

where $0.2^\circ$3 is the policy action, $0.2^\circ$4 is the base action scale, and $0.2^\circ$5 is an error-dependent gain.

This design preserves steady-state command offsets. If the arm requires a gravity-compensation offset, the policy can accumulate that offset in $0.2^\circ$6. When the action approaches zero at the target, the accumulated reference remains unchanged instead of being re-anchored to the measured joint state. The result is intended to prevent the arm from sagging or drifting after reaching the desired pose.

The reference offset is explicitly observed:

$0.2^\circ$7

This quantity provides information about the command state that would otherwise be hidden. Identical measured joints and target poses can produce different future dynamics depending on the currently accumulated reference. The paper therefore treats $0.2^\circ$8 as Markov-relevant.

The simulation observation has $0.2^\circ$9 dimensions and includes measured joint positions, joint velocities, target position, goal-relative keypoint errors, coarse and fine pose-error channels, running-best-error features, the reference offset $93.5\%$0, and the previous action. The hardware observation has $93.5\%$1 dimensions and includes analogous measured and target pose features.

Ablation results support the role of the accumulated reference. Full PolicyIK obtains $93.5\%$2 strict simulation success. Removing command-state feedback reduces success to $93.5\%$3, while re-anchoring the reference at the measured joints reduces strict success to $93.5\%$4, despite retaining $93.5\%$5 coarse success. This separation indicates that the reference mechanism primarily affects terminal precision and holding rather than coarse reaching.

3. Multiscale pose representation and adaptive gain

PolicyIK uses multiple pose-error representations to address the incompatible requirements of large-motion transport and millimeter-scale terminal regulation.

Keypoint pose representation

Three noncollinear offsets $93.5\%$6 attached to the end-effector produce point-position errors:

$93.5\%$7

In simulation, the offsets are $93.5\%$8 m along the end-effector axes. These keypoints encode translation and orientation jointly without relying exclusively on a rotation parameterization.

Coarse and fine feedback

The policy also observes pose errors in the current end-effector frame at two scales:

$93.5\%$9

The simulation scales are

$98.9\%$0

and

$98.9\%$1

The coarse representation supports large motions, whereas the fine representation expands the narrow terminal region in observation space. A $98.9\%$2 orientation residual occupies only a small fraction of the coarse $98.9\%$3 range but a substantial fraction of the fine $98.9\%$4 range.

Removing the fine channels increases median position error from $98.9\%$5 mm to $98.9\%$6 mm and reduces strict success. Without fine feedback, the policy can still reach the general vicinity of the target but loses sensitivity to the residuals that determine high-precision success.

Error-dependent action gain

A fixed action scale creates a speed–precision trade-off. Large actions accelerate distant motions but produce excessive terminal corrections; small actions improve resolution but make large movements slow. PolicyIK uses

$98.9\%$7

where

$98.9\%$8

The gain remains near one when either position or orientation error is large and decreases toward $98.9\%$9 near the target. Simulation parameters include $\pi_{0.5}$0, $\pi_{0.5}$1, $\pi_{0.5}$2, and $\pi_{0.5}$3.

Removing error-dependent scaling raises median entry time from $\pi_{0.5}$4 s to $\pi_{0.5}$5 s and lowers strict success. The results indicate that adaptive scaling complements fine feedback: fine features make small errors observable, while gain reduction makes those errors controllable.

4. Reward design and training

PolicyIK is trained as a goal-conditioned reinforcement-learning policy. Its reward combines tracking, progress, dwell, motion regularization, and joint-limit terms:

$\pi_{0.5}$6

A tolerance-normalized error is defined as

$\pi_{0.5}$7

The strict success region is $\pi_{0.5}$8. The running best error is

$\pi_{0.5}$9

The progress reward combines improvement in the running best, potential-based shaping, and a backslide penalty. The improvement term pays only when the policy achieves a new best normalized error, reducing incentives for oscillatory behavior that repeatedly revisits the same accuracy.

The dwell reward is

$95.7\%$0

Episodes do not terminate immediately upon first success. Instead, the policy receives reward for every step it remains within tolerance. Without the dwell reward, $95.7\%$1 of tasks that enter the tolerance subsequently leave it during the final window; with the full method, the corresponding rate is $95.7\%$2.

Motion regularization penalizes action changes and joint velocity:

$95.7\%$3

A separate term penalizes proximity to joint limits during the approach. This penalty is mainly active outside the terminal region, allowing the policy to use configurations near limits when necessary for final precision while discouraging premature saturation.

Simulation training

Simulation uses PPO with generalized advantage estimation in $95.7\%$4 parallel environments. Physics runs at $95.7\%$5 Hz and the policy at $95.7\%$6 Hz. The joint-position controller has stiffness $95.7\%$7, damping $95.7\%$8, finite effort limits, and $95.7\%$9 solver position iterations.

The reported training configuration includes:

• $q\in\mathbb{R}^{7}$0 epochs;
• approximately $q\in\mathbb{R}^{7}$1 transitions;
• two-layer actor and critic networks with $q\in\mathbb{R}^{7}$2 units and ELU activations;
• $q\in\mathbb{R}^{7}$3;
• GAE $q\in\mathbb{R}^{7}$4;
• PPO clip ratio $q\in\mathbb{R}^{7}$5;
• entropy coefficient $q\in\mathbb{R}^{7}$6;
• value coefficient $q\in\mathbb{R}^{7}$7;
• initial adaptive learning rate $q\in\mathbb{R}^{7}$8.

Training uses $q\in\mathbb{R}^{7}$9 sampled joint configurations. After collision and contact filtering, $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$0 configurations are used for starts and $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$1 for goals. The held-out evaluation set contains $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$2 disjoint start–goal pairs.

Physical training

Direct physical training uses FlashSAC, an off-policy SAC variant with hindsight experience replay. The reported configuration uses $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$3 online transitions, batch size $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$4, $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$5, target update rate $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$6, learning rate $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$7, $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$8 Hz control, and $T(q)=\operatorname{FK}(q)=(R(q),p(q))\in SE(3),$9-dimensional observations.

The hardware replay distribution combines demonstrations and online experience. Reverse curriculum learning begins with near-goal starts so that the policy first learns terminal correction and holding, after which the start range expands. A separate far-task pool includes rotations of $R(q)$0–$R(q)$1 and joint-space distances of at least $R(q)$2 rad. Hindsight relabeling includes the commanded goal, future achieved poses, and current achieved poses, with perturbations of $R(q)$3 mm and $R(q)$4 in a subset of terminal examples.

The hardware critic uses latent alignment: state-action and goal encoders produce representations whose elementwise squared difference is supplied to the critic. This is intended to represent temporal difficulty, including cases where a large joint-space detour is required even though instantaneous pose error is small.

5. Experimental results

Simulation

The primary simulation platform is a fixed-base 7-DoF OpenArm. PolicyIK is compared with UMI-RL, DLS, resolved-rate QP, and kinematic MPC.

Controller	Strict success	Coarse success	Median position error	Median orientation error
UMI-RL	$R(q)$5	$R(q)$6	$R(q)$7 mm	$R(q)$8
DLS	$R(q)$9	$1\,\mathrm{mm}$00	$1\,\mathrm{mm}$01 mm	$1\,\mathrm{mm}$02
QP	$1\,\mathrm{mm}$03	$1\,\mathrm{mm}$04	$1\,\mathrm{mm}$05 mm	$1\,\mathrm{mm}$06
MPC	$1\,\mathrm{mm}$07	$1\,\mathrm{mm}$08	$1\,\mathrm{mm}$09 mm	$1\,\mathrm{mm}$10
PolicyIK	$1\,\mathrm{mm}$11	$1\,\mathrm{mm}$12	$1\,\mathrm{mm}$13 mm	$1\,\mathrm{mm}$14
PolicyIK with deployment	$1\,\mathrm{mm}$15	$1\,\mathrm{mm}$16	$1\,\mathrm{mm}$17 mm	$1\,\mathrm{mm}$18

PolicyIK remains within both thresholds at every sample of the final second on $1\,\mathrm{mm}$19 of tasks. On successful tasks, median net end-effector motion during that final second is $1\,\mathrm{mm}$20 and $1\,\mathrm{mm}$21.

Classical controllers fail disproportionately near joint limits. Such cases account for $1\,\mathrm{mm}$22–$1\,\mathrm{mm}$23 of their strict failures. PolicyIK achieves approximately $1\,\mathrm{mm}$24 strict success on the corresponding difficult subset.

Deployment protocol

A failed attempt can be retried. If the final error is within $1\,\mathrm{mm}$25 cm, the system corrects the goal using the negative residual position and inverse residual rotation. More distant failures receive up to eight attempts with a transient goal consisting of a random $1\,\mathrm{mm}$26-m positional displacement and a $1\,\mathrm{mm}$27 random-axis rotation for the first $1\,\mathrm{mm}$28 steps, followed by the original target.

Checkpoint averaging improves single-attempt strict success from $1\,\mathrm{mm}$29 to $1\,\mathrm{mm}$30. Error-corrected goals raise it to $1\,\mathrm{mm}$31, and transient-goal retries raise it to $1\,\mathrm{mm}$32, with an average of $1\,\mathrm{mm}$33 attempts per task. Remaining failures cluster near joint limits: the worst goal joint is a median $1\,\mathrm{mm}$34 of its range from a limit, compared with $1\,\mathrm{mm}$35 for first-attempt successes.

Physical OpenArm

PolicyIK is trained directly on a physical 7-DoF OpenArm. At a $1\,\mathrm{mm}$36-second budget, the task requires reaching and holding within $1\,\mathrm{mm}$37 mm and $1\,\mathrm{mm}$38 for the final five seconds.

Controller	Reached	Held for final $1\,\mathrm{mm}$39 s	Median position error	Median orientation error
DLS	$1\,\mathrm{mm}$40	$1\,\mathrm{mm}$41	$1\,\mathrm{mm}$42 mm	$1\,\mathrm{mm}$43
Resolved-rate QP	$1\,\mathrm{mm}$44	$1\,\mathrm{mm}$45	$1\,\mathrm{mm}$46 mm	$1\,\mathrm{mm}$47
Kinematic MPC	$1\,\mathrm{mm}$48	$1\,\mathrm{mm}$49	$1\,\mathrm{mm}$50 mm	$1\,\mathrm{mm}$51
Adapted OpenArm QP	$1\,\mathrm{mm}$52	$1\,\mathrm{mm}$53	$1\,\mathrm{mm}$54 mm	$1\,\mathrm{mm}$55
PolicyIK	$1\,\mathrm{mm}$56	$1\,\mathrm{mm}$57	$1\,\mathrm{mm}$58 mm	$1\,\mathrm{mm}$59

PolicyIK reaches $1\,\mathrm{mm}$60 of tasks and holds $1\,\mathrm{mm}$61, whereas the classical controllers hold at most $1\,\mathrm{mm}$62. At a $1\,\mathrm{mm}$63-second budget, PolicyIK reaches $1\,\mathrm{mm}$64 tasks and holds for five seconds on $1\,\mathrm{mm}$65.

The main advantage is sustained regulation. Classical controllers may reach the target but continue correcting around it or drift outside the narrow tolerance. Accumulated references allow PolicyIK to maintain the learned steady-state command once correction is no longer required.

Cross-embodiment xArm7 evaluation

On an xArm7, both simulation-trained and hardware-trained PolicyIK achieve $1\,\mathrm{mm}$66 successes for standard reaching and large rotations. For large rotations, DLS, QP, and MPC achieve $1\,\mathrm{mm}$67, while the xArm built-in IK achieves $1\,\mathrm{mm}$68.

The reported large-rotation median errors are:

• simulation-trained PolicyIK: $1\,\mathrm{mm}$69 mm and $1\,\mathrm{mm}$70;
• hardware-trained PolicyIK: $1\,\mathrm{mm}$71 mm and $1\,\mathrm{mm}$72.

These results support transfer of the formulation and control interface, which require joint state, forward kinematics, pose goals, and a joint-position execution layer. They do not establish that a single network transfers without embodiment-specific training or adaptation.

VLA execution

PolicyIK is evaluated as the low-level executor for the $1\,\mathrm{mm}$73 VLA policy in ten adapted LIBERO-Object pick-and-place tasks. The VLA emits relative end-effector commands at $1\,\mathrm{mm}$74 Hz, while PolicyIK executes pose commands at $1\,\mathrm{mm}$75 Hz.

Reported success rates are:

• default DLS: $1\,\mathrm{mm}$76;
• hand-tuned DLS: $1\,\mathrm{mm}$77;
• hand-tuned QP: $1\,\mathrm{mm}$78;
• PolicyIK: $1\,\mathrm{mm}$79.

Near the robot mount, where a shoulder joint approaches its limit, PolicyIK achieves $1\,\mathrm{mm}$80, compared with $1\,\mathrm{mm}$81 for default DLS and $1\,\mathrm{mm}$82 for hand-tuned QP. The evaluation suggests that PolicyIK can preserve a common Cartesian action interface for a high-level VLA policy while absorbing embodiment-specific feasibility and execution effects at the low level.

6. Limitations and significance

PolicyIK is a learned closed-loop IK controller, not a general motion planner. It does not itself provide global collision-free planning, obstacle avoidance, contact planning, or task-level sequencing. It requires a working forward-kinematics model, joint-state feedback, a pose goal, and a joint-position execution layer.

Performance remains sensitive to reachability and joint limits. The deployment protocol improves difficult cases but does not eliminate failures near configurations where the required reference offset lies beyond a joint limit. Physical training also requires $1\,\mathrm{mm}$83 online transitions, demonstrations, resets, and replay engineering. External contacts, encoder bias, tool deformation, perception errors, and substantial model mismatch are not fully evaluated.

The approach is not a universal embodiment-independent policy. Experiments on OpenArm and xArm7 support reuse of the formulation and interface, but separate training or adaptation is still employed. The policy also depends on the quality of the fixed-gain joint controller and on the representation of pose feedback.

The principal contribution is architectural: PolicyIK combines learned inverse mapping with learned execution compensation. Its key design elements are:

1. Accumulated joint references, which preserve gravity- and controller-dependent offsets.
2. Reference-minus-measured-joint observation, which exposes command-state information.
3. Coarse and fine pose feedback, which jointly support large movements and millimeter-scale regulation.
4. Error-dependent action gains, which provide high terminal resolution without sacrificing transport speed.
5. Progress and dwell rewards, which separately encourage reaching and sustained containment.
6. Dynamics-aware reinforcement learning, which incorporates physical execution effects rather than treating IK as purely geometric.
7. Goal-conditioned and hierarchical training procedures, including PPO in simulation, FlashSAC and hindsight experience replay on hardware, reverse curricula, and far-task sampling.

Within the reported evaluation, these mechanisms yield substantially higher high-precision success than DLS, QP, and MPC under strict terminal and holding criteria. The paper’s broader implication is that reinforcement learning can learn not only a mapping from Cartesian poses to joint configurations, but also the reference offsets, residual corrections, and closed-loop holding behavior required to execute those poses accurately on real robot arms (Liu et al., 3 Nov 2026).