PAKT: Physically-Aligned Kinesthetic Teaching

Abstract

Real-world reinforcement learning systems still struggle with contact-rich industrial manipulation, where tasks require micrometer-level precision, high success rates, human-level cycle times, and guidance that operators can provide safely and intuitively.

PAKT combines constrained kinesthetic teaching with a reference-generator and high-frequency impedance-control stack so human demonstrations remain feasible for the learned policy. Across four insertion and assembly benchmarks, it reduces cycle time by 23-48% and human intervention by 60-85%.

Video

Project video showing the PAKT workflow for contact-rich robot learning.

PAKT combines direct kinesthetic guidance with the same constrained execution stack used by the learned policy.

Contributions

Concrete system contributions for physically aligned kinesthetic teaching in real-world reinforcement learning.

Policy-feasible kinesthetic teaching

Operator-applied forces are routed through constrained admittance control, allowing direct physical guidance while shaping demonstrations with the same action parameterization and motion limits used during autonomous rollout.

High-frequency execution stack

Cartesian delta commands are issued at policy rate, shaped by a third-order reference generator, and tracked by a compensated 1 kHz Cartesian impedance controller.

Real-world ablation and evaluation

The evaluation separates controller-stack effects from kinesthetic-guidance effects across four contact-rich insertion and industrial assembly tasks.

Control Path

Switch between a sampled policy target and sinusoidal human-input wrench, then inspect how the selected signal passes through reference generation, impedance control, and the simulated end effector.

Policy signal

Amplitude A Signal frequency f Policy rate

External wrench

Force amplitude Force frequency

Admittance Controller

Admittance mass Admittance damping Admittance stiffness

Switch

Reference Generator

Bandwidth ω Velocity limit Acceleration limit Jerk limit

Reference output

Impedance Controller

Impedance controller

τ_{imp} = {J (q)}^{T} (Λ {\ddot{x}}_{ref} + D_{x} (Λ, K_{x}) \tilde{\dot{x}} + K_{x} \tilde{x} - Λ \dot{J} (\dot{q}) \dot{q} + 0.5 \dot{Λ} \tilde{\dot{x}})

τ_{null} = N (D_{null} \tilde{\dot{q}} + K_{null} \tilde{q})

τ_{d} = τ_{imp} + τ_{null} + C (q, \dot{q}) \dot{q} + g (q)

C2	$f_{imp} = D_{x} (M, J) \dot{x} + K_{x} e$
C3	$f_{imp} = D_{x} \dot{x} + K_{x} e$
C4	$f_{imp} = D_{x} \dot{x} + K_{x} e + \int k_{i} e d t$
C5	$f_{imp} = D_{x} \dot{x} + K_{x} clip (e, e_{lim})$

Here x tilde = Log(T_ref T_EE^-1), matching the paper's Cartesian pose error.

Inertia scale Stiffness Kx Damping ζ

End effector trajectory

Joint torque limit Sensor low-pass

Controller Comparison

Tracking and contact behavior for sampled motion across the implemented controller variants.

Kinesthetic Guidance

Move the simulated arm directly and inspect how human input is converted into constrained motion.

RL Reach Training

A simplified in-browser sparse-reward reach task inspired by the RAM training workflow, with replay, demonstrations, and policy-compatible interventions.

idle waiting for replay intervention inactive

Experimental Setup

Hardware, sensing, and task imagery for the four insertion benchmarks.

Franka robot setup across the four insertion tasks — Franka Emika robot with wrist-mounted RealSense cameras across the task setups.

Robot Franka Emika Robot with Franka Hand end effector

Control compute NVIDIA Jetson Orin AGX running the 1 kHz controller stack

Policy compute Desktop workstation with NVIDIA RTX 4090 for policy and success classifier

Perception Two Intel RealSense D405 wrist cameras, downsampled for policy input

FMB Peg

Benchmark peg insertion with the target location outlined.

RAM Stick

Contact-rich electronics insertion repeated over five random seeds.

Limit Fixture

Industrial fixture assembly with tight final alignment.

Busbar

Rigid busbar insertion in the same industrial workflow.

Results

Controller behavior is separated from reinforcement-learning outcomes and task-level metrics.

Controller behavior

Controller tracking error and contact force comparison — Tracking errors are low-pass filtered at 7 Hz for visibility; the closest ablation preserves similar free-space tracking, while simpler controller variants increase tracking error or rely on clipping that causes lag. In the contact test, the proposed stack yields the smallest peak force overall, whereas simpler variants produce substantially higher reaction forces.

Controller Comparison Metrics

Tracking traces are low-pass filtered at 7 Hz for visibility. Peak contact force is measured in the 10 Hz command/check protocol used by the controller comparison.

Controller	x error [mm]	y error [mm]	z error [mm]	Peak contact force [N]
C1: PAKT proposed stack	16.8	14.1	9.6	22.5
C2: no inertia / desired velocity	16.6	14.1	9.6	33.9
C3: manual damping	24.8	22.5	16.2	46.5
C4: integral action	24.8	22.4	16.0	45.03
C5: clipped error	100.5	37.2	16.8	28.15

Learning outcomes

Reward, cycle time, and intervention rate over training — The curves compare the baseline, the hybrid controller variant, and PAKT across reward, cycle time, and intervention rate; RAM insertion reports mean and standard deviation across five seeds, while the other tasks are single real-world runs. Across tasks, PAKT reduces cycle time by 23-48%, demonstration time by 15-34%, and cumulative interventions by 60-85%.

Final Learning Metrics

Baseline is HIL-SERL with SpaceMouse. Hybrid uses the PAKT controller stack with SpaceMouse. PAKT uses the proposed controller stack with kinesthetic guidance. RAM reports five random seeds; other tasks are single real-world runs. Cumulative intervention count is the area under the intervention-rate curve.

Task	Baseline: HIL-SERL + SpaceMouse				Hybrid: PAKT controller + SpaceMouse				PAKT: controller + kinesthetic guidance
Task	Demo time [s]	Success rate	Cycle time [s]	Interventions	Demo time [s]	Success rate	Cycle time [s]	Interventions	Demo time [s]	Success rate	Cycle time [s]	Interventions
Peg	216	1.0	3.88	6276	199	1.0	2.25	2690	183	1.0	2.17	980
RAM stick	243	0.88	5.2	8780	219	0.99	4.07	5205	182	0.98	4.0	3325
Limit fixture	209	0.99	3.01	5937	194	0.98	1.87	2026	177	0.99	1.92	1342
Busbar	221	0.85	3.91	9286	187	0.98	2.09	2920	146	0.99	2.03	1327

PAKT: Physically-Aligned Kinesthetic Teaching for Reinforcement Learning