Kinematic Reward, Measured Effort: Hardware-Validated RL Morphology Optimization of a Planar 2R Manipulator

Gunesh Gupta; Arvind Kumar Mishra; Sohom Chakrabarty

cs.ROOct 11, 2026

Kinematic Reward, Measured Effort: Hardware-Validated RL Morphology Optimization of a Planar 2R Manipulator

Authors: Gunesh Gupta, Arvind Kumar Mishra, Sohom Chakrabarty

Organizations: Independent Researcher, Haridwar, India · Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee, India

Abstract

Yoshikawa's Manipulability Index is generally used as a classical measure to define an optimal morphology of a manipulator. However, any such optimization is almost always studied as a purely kinematic quantity in simulation and is rarely validated on hardware. We present a reinforcement-learning framework with RSL-RL PPO that optimizes the morphology of a 2R SCARA-type manipulator arm with Yoshikawa's kinematic manipulability index as a core reward, and the analytically derived closed-form optimum for the circular task is used to verify that our method recovers it. Then the same method is applied to custom elliptical and rectangular paths having no analytical optimum. The RL-optimized morphologies are then transferred to a 2R hardware manipulator to validate its effect in reduction of joint load in the hardware. Compared to the worst morphology, the optimum morphology delivered by our method reduces second joint load by 38.4 +/- 0.6% for the ellipse path and 41.3 +/- 0.3% for the rectangle, and first joint load by 15%.

Figures & tables

Fig. 1 : The three task paths: circle (held at radius

R

), ellipse, and rectangle.

Fig. 2 : Mean second-joint torque vs. manipulability

w

over a dense morphology sweep (simulation, EE mass

+60

g): ellipse (top), rectangle (bottom), with the

\tau_{2}\propto w^{-p}

fit and OPT/MID/WC marked (from Section V-B ).

Term / role	Ellipse	Rectangle
manipulability $\|\sin\theta_{2}\|$ , $w_{\mathrm{manip}}$	$0.5$	$0.5$
tracking $w_{\mathrm{t}}$ (bandwidth $\alpha$ )	$1.0$ ( $2500$ )	$1.0$ ( $2500$ )
length reg. $w_{\ell}$	$0.5$	$0.5$
corner floor $w_{\mathrm{floor}}$ ( $\delta$ )	—	$0.2$ ( $0.5$ )
settle ramp $\gamma_{\max}$	$2.0$	$6.0$
slider speed $w_{s}$	—	$0.3$

TABLE I : Reward weights for the trajectory tasks, code-verified against each branch. The ellipse uses the common reward chassis. The rectangle adds two terms (corner floor, slider speed) and retunes two (

\gamma_{\max}

, action rate).

Panel of Figure 4 — Fig. 3 : Hardware platform: (a) Planar 2R arm; (b) prismatic link stage; (c) the $60$ g end-effector payload.

Task		$\bar{w}$	$\min$ $\|\sin\theta_{2}\|$	Sim $\overline{\|\tau_{2}\|}$ [N $\cdot$ m]	HW $\overline{\|j_{2}\|}$ [%]	$\overline{\|\text{track}_{\text{error}}\|}$ [mm]
Ellipse	OPT	0.030	0.84	0.20	8.74 $\pm$ 0.08	16.6 $\pm$ 0.0
	MID	0.022	0.62	0.27	11.10 $\pm$ 0.05	17.8 $\pm$ 0.0
	WC	0.016	0.30	0.36	14.18 $\pm$ 0.02	19.1 $\pm$ 0.0
Rect.	OPT	0.032	0.86	0.22	10.29 $\pm$ 0.06	18.6 $\pm$ 0.0
	MID	0.024	0.60	0.31	13.53 $\pm$ 0.04	21.6 $\pm$ 0.0
	WC	0.018	0.25	0.42	17.53 $\pm$ 0.03	30.2 $\pm$ 0.1

TABLE II : Per-morphology summary. Hardware values are the mean over ten repeated runs (one standard deviation shown), EE mass

+60

g both simulation and hardware.

Fig. 4 : OPT/MID/WC comparison: (a) simulated mean second-joint torque [N

\cdot

m]; (b) measured hardware second-joint load [%, relative, averaged over 10 runs]. Both rank OPT

\,<\,

MID

\,<\,

WC (Section V-C ).

Panel of Figure 7 — Fig. 5 : Plots of $|\bar{j}_{2}|$ load % and $w(\theta_{2})$ over 2 loops averaged across 10 runs.

Robotic Optimization

See all 31 papers

Morphology and actuation as inductive biases in robotic hand manipulation
Sep 4, 2026Zalán Tari, Eszter Birtalan, Péter Polcz +1Robotics Robotic Hand Design
Pázmány Péter Catholic University, Faculty of Information Technology and Bionics, Budapest, Hungary
Energy-Regularized Imitation Learning for Force- and Work-Aware Robotic Manipulation
Sep 16, 2026Toshiki Otani, Hiromu Taketsugu, Norimichi UkitaRobotic RL Robotic Manipulation
Toyota Technological Institute, Japan
RARM: Confidence-Gated Progress Reward Modeling for RL in Manipulation
Jun 20, 2026Pengzhi Yang, Xinyu Wang, Pengyu Jing +7Long-Horizon Robotic Manipulation Robot Skill Learning
NUS Human-Centered Robotic Lab · ‡ Booking.com · University of Cambridge +1

Sep 4, 2026J/K move · Enter open · S save

Morphology and actuation as inductive biases in robotic hand manipulation

Zalán Tari, Eszter Birtalan, Péter Polcz, Miklós Koller

Pázmány Péter Catholic University, Faculty of Information Technology and Bionics, Budapest, Hungary

Robotics Robotic Hand Design Robotic Manipulation Robotic Control

Open paper AskPDF arXiv

Robotic hands vary widely in anatomical fidelity and mechanical complexity, and these structural choices influence the coordination of joint motions and the difficulty of controlling the system. A unified framework is presented in which the kinematic and actuation stages are analysed separately and in composition, through the conditioning of the task Jacobian, the actuation matrix, and their product. It is applied to two hands representing opposing design philosophies, the Shadow Dexterous Hand and the Anatomically Correct, Biomechatronic Hand, along four morphological aspects: joint axis geometry, actuator-to-DOF ratio, coupling architecture, and authority distribution. All parameters are derived from the hands' canonical digital representations. Anatomical fidelity carries no uniform advantage: oblique axes improve thumb conditioning but leave the long fingers worse conditioned than the orthogonal-axis design, while the branching tendon network improves the effective control mapping at every long finger and worsens it significantly at the thumb, where actuator authority is concentrated on thumb opposition. Predictions derived from these metrics are evaluated against reinforcement learning experiments using PPO, DDPG+HER, and TQC+HER, across three different tasks.

Abstract

Robotic Optimization

Explore similar work

Morphology and actuation as inductive biases in robotic hand manipulation

Energy-Regularized Imitation Learning for Force- and Work-Aware Robotic Manipulation

RARM: Confidence-Gated Progress Reward Modeling for RL in Manipulation