PolicyIK: High-Precision Inverse Kinematics for Robot Arms with Reinforcement Learning

Yuhan Liu; Xinqi Liu; Zixuan Dong; Keith W. Ross; Shenji Wan

cs.RONov 3, 2026

PolicyIK: High-Precision Inverse Kinematics for Robot Arms with Reinforcement Learning

Authors: Yuhan Liu, Xinqi Liu, Zixuan Dong, Keith W. Ross, Shenji Wan

Organizations: New York University · New York University Abu Dhabi

Abstract

Inverse kinematics (IK) converts end-effector pose commands into joint motion, and many vision-language-action (VLA) policies rely on it to act on a given arm and to transfer across embodiments. Precise IK remains laborious: redundancy and singularities complicate the inverse mapping, execution depends on hand-tuned controllers, and training data on physical robots are costly to collect. We present PolicyIK, a goal-conditioned reinforcement learning policy for high-precision IK. It updates joint-position references from pose feedback and observes its accumulated reference relative to the measured joints, so it can retain the offset that the position controller needs at rest. Two-scale pose errors with an error-dependent action gain resolve millimeter residuals while preserving large motions. Progress and dwell rewards teach it to both reach the tolerance and stay within it. In simulation, a single attempt by the trained PPO policy keeps the mean errors over the final second within 1 mm and 0.2° on 93.5% of held-out tasks, and a deployment protocol raises success to 98.9%. When trained directly on a physical arm with an off-policy RL learner, PolicyIK achieves higher reaching and holding success than all four classical IK controllers under the same time budgets. In simulated pick-and-place, PolicyIK executes the end-effector commands of the $π_{0.5}$ VLA policy with 95.7% success. These results show that reinforcement learning can provide high-precision inverse kinematics for robot arms. Code is available at https://github.com/Tinaliu0123/PolicyIK.

Figures & tables

Figure 1: PolicyIK: from broad reaching to precise regulation. (a) Full-pose reaching across the simulated workspace. (b) Reaching and holding within 1 mm and $0.2^{\circ}$ . (c) On hardware, PolicyIK holds the pose within 1 mm and $0.2^{\circ}$ throughout the final 5 s on more tasks than classical controllers.

Figure 2: PolicyIK control formulation. At each step, the policy maps the observation to a joint-reference increment, which is scaled by the error-dependent gain, accumulated in the joint reference, and tracked by a joint PD controller. Colored blocks are the designs of Sections 4.1 to 4.3 .

			Median error
Controller	Strict (%) $\uparrow$	Coarse (%) $\uparrow$	Pos. (mm) $\downarrow$	Ori. ( ∘ ) $\downarrow$	$E[N]$
UMI-RL (tuned)	0.00 $\pm$ 0.00	16.38 $\pm$ 3.10	16.65 $\pm$ 0.80	4.25 $\pm$ 0.77	1.000
DLS	$50.41$	$64.42$	$0.94$	$0.15$	1.000
QP	$56.21$	$63.98$	$0.57$	$0.11$	1.000
MPC	$56.33$	$64.78$	$0.54$	$0.10$	1.000
PolicyIK	93.49 $\pm$ 0.20	96.56 $\pm$ 0.16	0.25 $\pm$ 0.02	0.04 $\pm$ 0.00	1.000

Table 1: Simulation results. With deployment, each task reports its first strictly successful attempt, or its last attempt if none succeeds, and

E[N]

is the mean number of attempts. DLS, QP, and MPC are tuned on a separate set of tasks from the same distribution (Appendix E ).

Figure 3: Ablations on command-state feedback, pose feedback and gain, and rewards. Curves show the share of test tasks within 1 mm and

0.2^{\circ}

at each time step.

Table 3: Reaching, holding, and median pose errors on 60 physical tasks within 25 s. The best result is in bold, and the second-best is underlined.

Figure 6: A case in which MPC jitters around the goal after reaching, while PolicyIK holds.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Strict (%) $\uparrow$	$E[N]$
Final checkpoint, single attempt	92.30 $\pm$ 0.13	1.000
Checkpoint average, single attempt	93.49 $\pm$ 0.20	1.000
$+$ error-corrected goal	94.80 $\pm$ 0.12	1.036
$+$ transient-goal attempts	98.92 $\pm$ 0.23	1.212

Appendix

Table 4: Strict success as checkpoint averaging and the two deployment steps are added.

E[N]

is the mean number of attempts per task.

		Median error $\downarrow$
Setting	Coarse (%) $\uparrow$	Pos. (mm)	Ori. ( ∘ )
0.20 s horizon, $k=1$ (source)	0.04 $\pm$ 0.01	19.45 $\pm$ 3.80	74.69 $\pm$ 2.62
0.54 s horizon, $k=1$	0.02 $\pm$ 0.02	6.27 $\pm$ 0.43	54.87 $\pm$ 3.85
0.54 s horizon, $k=0.5$	0.35 $\pm$ 0.09	11.17 $\pm$ 2.27	37.45 $\pm$ 0.61
0.54 s horizon, $k=0.25$	16.38 $\pm$ 3.10	16.65 $\pm$ 0.80	4.25 $\pm$ 0.77
3.3 s horizon, $k=0.1$	1.04 $\pm$ 0.06	44.16 $\pm$ 3.52	4.20 $\pm$ 1.25

Appendix

Table 5: Tuned variants of UMI-RL. Entries are means and standard deviations across three training seeds. Position and orientation errors are median terminal-window errors. The factor

k

scales the orientation ladder of the source recipe. Strict success is zero in every setting.

Controller	Strict (%) $\uparrow$	Coarse (%) $\uparrow$	Pos. (mm)	Ori. ( ∘ )
			Median error $\downarrow$
DLS, selected ( $k=2$ , 0.15 rad lead)	50.41	64.42	0.94	0.15
QP, selected ( $k=1.5$ , 0.15 rad lead)	56.21	63.98	0.57	0.11
MPC, selected ( $k=1.5$ , 0.15 rad lead)	56.33	64.78	0.54	0.10
DLS, measured-joint anchor, full step	1.84	46.50	4.74	2.20
DLS (default), 30 Hz	1.60	42.86	5.88	2.73

Appendix

Table 6: Classical controllers on the 4,120 test tasks. The selected settings appear in Table 1 . DLS (default) is the Isaac Lab differential IK controller with its default settings, as in Section 5.1.3 .

Figure 7: One test task. Left: intervals in which each joint lies within 0.01 rad of its lower (dark) or upper (light) limit. Right: position and orientation errors, with the strict tolerances dashed. The dotted line marks when a third QP joint reaches its limit (1.7 s). The QP failure coincides with this sustained limit occupancy, and its error then stays near 96 mm and

8^{\circ}

. PolicyIK never reaches a joint limit and enters the strict tolerance at 2.0 s.

Command-state feedback and reference anchor
	Success (%) $\uparrow$		Terminal phase $\downarrow$		Median error $\downarrow$
Variant	Coarse	Strict	Entry (s)	Uncont. (%)	Pos. (mm)	Ori. ( ∘ )
PolicyIK	96.56 $\pm$ 0.16	93.49 $\pm$ 0.20	1.73 $\pm$ 0.01	2.43 $\pm$ 0.23	0.25 $\pm$ 0.02	0.04 $\pm$ 0.00
w/o command-state feedback	92.63 $\pm$ 0.20	84.26 $\pm$ 0.28	2.04 $\pm$ 0.02	10.32 $\pm$ 0.32	0.30 $\pm$ 0.00	0.06 $\pm$ 0.00
measured-joint anchor	95.90 $\pm$ 0.17	30.77 $\pm$ 7.94	1.80 $\pm$ 0.03	82.46 $\pm$ 6.62	1.27 $\pm$ 0.05	0.16 $\pm$ 0.01
Pose feedback and action scaling

Appendix

Table 7: Component ablations with one attempt per task and matched training budgets. Entry is the median first-entry time and Uncont. the uncontained share (Appendix C ). The measured-joint anchor sets

z_{t-1}=q_{t}

in Equation 2 and removes command-state feedback, and the fixed gain is

\beta=0.1

Targets	DLS (default)	DLS (hand-tuned)	QP (hand-tuned)	PolicyIK
Closest to the mount	85.5	96.8	85.9	95.1
Farther to the side	96.1	96.5	95.7	96.4

Appendix

Table 8: Pick-and-place success (%) by target location, three runs from each of the 50 official initial states per task (750 episodes per group).

Figure 8: (a) The FlashSAC network, used for the actor and, in FlashSAC, for each critic. Filled circles mark the hyperspherical normalization ( Lee et al., 2025 ) , where weight vectors project onto the unit sphere after every gradient step. (b) The latent-alignment critic that PolicyIK uses on hardware (Appendix H.2 ). In both panels,

p_{\omega}(o_{t},a_{t})

denotes the value-distribution logits that the critic’s linear head outputs; a softmax over the atoms turns them into the probabilities

p_{\omega,i}

of Equation 15 .

	15 s budget			25 s budget
Policy	Reached	Held 1 s	Held 5 s	Reached	Held 1 s	Held 5 s	Coarse	Gross
Ablated	40	36	31	46	43	40	52	5
PolicyIK	52	44	27	54	45	43	59	1

Appendix

Table 9: Ablation of the hardware components on 60 physical OpenArm tasks. The Ablated policy excludes the latent-alignment critic, far-task selection by joint-space distance, and the relaxed reference bound. Reached and held use the criteria defined in the main body. Coarse counts tasks whose final-second errors are within 1 cm and

2^{\circ}

, and gross counts tasks that end more than 20 mm from the goal, both at the 25 s budget. Bold marks the better result.

	15 s budget			25 s budget
Controller	Reached	Held 1 s	Held 5 s	Reached	Held 1 s	Held 5 s
DLS	38	21	6	48	29	17
Resolved-rate QP	43	21	6	48	24	16
Kinematic MPC	29	10	3	46	26	15
Adapted OpenArm QP	13	8	1	32	16	11
PolicyIK	52	44	27	54	45	43

Appendix

Table 10: Reaching and final-window holding counts out of 60 OpenArm tasks, with best results in bold and second-best results underlined.

Setting	PolicyIK on hardware	FlashSAC
Learner
Online transitions	120,000
Batch size	1,024	2,048
Replay capacity	120,000 (the whole run)	$10^{6}$
Initial random actions	200	–
Updates begin after	1,024 transitions	–

Appendix

Table 11: Settings for training PolicyIK on hardware, used for both the OpenArm and the xArm7. The FlashSAC column lists the corresponding settings of FlashSAC ( Kim et al., 2026 ) ; a dash marks a setting that FlashSAC does not specify.

Controller	Formulation	Parameters
DLS	Damped least squares with global speed scaling	$k=2$ , $\lambda=0.02$
Resolved-rate QP	Damped least squares within the joint bounds	$k=3$ , $\lambda=0.005$
Kinematic MPC	Seven-step receding horizon (0.14 s)	$k=3$ , $\lambda=0.005$
Adapted OpenArm QP	OpenArm QP with measured-pose settling	Costs 12/1.5, damping 0.1

Appendix

Table 12: Classical hardware baselines. All four map the measured joint state and the goal pose to joint-position references at 50 Hz within the joint limits and the 0.20 rad/s reference-speed bound. DLS, QP, and MPC weight rotation errors by 0.2 relative to translation.

Standard reaching
Controller	Success	Reach (s)	Position (mm)	Orientation ( ∘ )
DLS	60/60	2.9	0.074	0.015
QP	60/60	2.0	0.094	0.018
MPC	60/60	2.3	0.085	0.016
xArm built-in IK	59/60	1.8	0.004	0.001
PolicyIK (sim-trained)	60/60	2.2	0.169	0.034

Appendix

Table 13: Physical xArm7 evaluation on two sets of 60 tasks each. Reach-time medians use reached tasks.

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Inverse kinematics (IK) remains a critical bottleneck for real-time robot manipulation. Classical numerical solvers achieve high geometric precision but often suffer from discontinuous branch switching and unstable behavior near kinematic singularities during closed-loop deployment. Meanwhile, learned IK approaches frequently struggle to balance spatial accuracy, motion smoothness, and real-time efficiency, particularly when trained on noisy human teleoperation data. We present MimicIK, a real-time generative inverse kinematics framework that learns smooth and robust joint-space motion priors from teleoperation demonstrations through conditional flow matching. Given the current joint configuration and a target end-effector pose, MimicIK predicts continuous delta-joint commands using an efficient two-step iterative refinement process based on a Minimal Iterative Policy (MIP) backbone. To enforce physical consistency, we further introduce an FK consistency loss, a differentiable forward-kinematics regularization that penalizes task-space deviations from the target pose during training. We evaluate MimicIK on a real-world 6-DOF robot dataset containing 8,848 teleoperation demonstrations. MimicIK achieves a mean position error of 4.65 mm, a 10 mm success rate of 92.01%, and a trajectory spike rate of only 7.99%. Compared with a UNet diffusion baseline, our method improves both spatial accuracy and motion smoothness while reducing inference latency from 21.66 ms to 6.74 ms. Furthermore, unlike deterministic MLP baselines that catastrophically diverge under out-of-distribution deployment, MimicIK remains stable near singular configurations and enables robust 20 Hz real-time control on deployment hardware.

Abstract

Inverse Kinematics

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