Reinforcement learning (RL) has achieved strong performance in robotic control; however, state-of-the-art policy learning methods, such as actor-critic methods, still suffer from high sample complexity and often produce physically inconsistent actions. This limitation stems from neural policies implicitly rediscovering complex physics from data alone, despite accurate dynamics models being readily available in simulators. In this paper, we introduce a novel physics-informed RL framework, called PIPER, that seamlessly integrates physical constraints directly into neural policy optimization with analytical soft physics constraints. At the core of our method is the integration of a differentiable Lagrangian residual as a regularization term within the actor's objective. This residual, extracted from a robot's simulator description, subtly biases policy updates towards dynamically consistent solutions. Crucially, this physics integration is realized through an additional loss term during policy optimization, requiring no alterations to existing simulators or core RL algorithms. Extensive experiments demonstrate that our method significantly improves learning efficiency, stability, and control accuracy, establishing a new paradigm for efficient and physically consistent robotic control.
Figures & tables
Figure 1: Comparison of architecture and performance between SAC and Physical-Informed SAC . (a) The standard SAC framework relying solely on the MuJoCo simulator, resulting in High Error in the robotic arm task. (b) The Physical-Informed SAC framework which incorporates an Analytic Physics & Constraints module, leading to Low Error and precise control.
Figure 2: Overview of the physics-informed actor–critic reinforcement learning framework. The actor policy generates control actions based on the current system state, while the critic network evaluates action quality by estimating the value function. A PINN, coupled with a high-fidelity simulator (MuJoCo), embeds prior physical laws and system dynamics into the learning loop, providing physically consistent state transitions and constraints. The interaction between data-driven policy optimization and physics-based modeling improves training stability, sample efficiency, and generalization performance compared to purely data-driven reinforcement learning approaches.
Method
Model-Free
No Test-Time Optimization
Algorithm Agnostic
Uses Lagrangian Structure
PPO / SAC / TD3
✓
✓
✓
×
Deep Lagrangian ( Lutter et al., 2019 )
×
✓
×
✓
Residual RL ( Johannink et al., 2019 )
✓
✓
✓
×
Safety Layer / CPO ( Dalal et al., 2018 )
✓
×
×
×
HJB-RL ( Cheng et al., 2021 )
✓
×
×
×
PI-MBRL ( Ramesh and Ravindran, 2023 )
×
✓
×
×
Table 1: Comparison of physics-aware reinforcement learning approaches.
Figure 3: Qualitative comparison of final end-effector configurations in the FetchReach-v4 environment. The green background indicates the simulated MuJoCo workspace. Top row: Baseline policies often exhibit steady-state error or drift due to lack of structural knowledge. Bottom row: PIPER policies achieve tighter convergence to the target geometry by exploiting the null space of the manipulator dynamics.
Algorithm
Success Rate
Final Error
Precision Gain
Stability ( σ )
Stability Gain
Steps to 95%
Efficiency Gain
PPO
100%
9.35 mm
–
10.94
–
46,650
–
PIPER-PPO
100%
8.02 mm
+14.2%
8.13
+25.7%
32,800
+30%
TD3
100%
16.56 mm
–
17.59
–
23,850
–
PIPER-TD3
100%
3.39 mm
+79.5%
11.53
+34.5%
17,550
+26%
SAC
100%
7.55 mm
–
11.41
–
24,250
–
PIPER-SAC
100%
2.15 mm
+71.5%
8.10
+29.0%
13,250
+45%
Table 2: Performance Metrics for FetchReach-v4 . PIPER improves efficiency, precision, and stability across PPO, TD3, and SAC.
Figure 4: FetchReach Learning Dynamics. Comparison of baseline and our physics-informed variants (shaded regions represent ±1 standard deviation across 5 random seeds). Our PIPER-SAC ( orange ) demonstrates superior convergence speed by exploiting the inertial null-space. Zoom in to view better details.
Figure 5: Performance Analysis across Contact-Rich Environments. Comparison of Baseline TQC+HER vs. PIPER-TQC. Zoom in to view better details.
Task
Algorithm
Success Rate
Final Error
Precision Gain
Stability ( σ )
Stability Gain
Sample Efficiency
Efficiency Gain
FetchPush
TQC+HER
98%
12.4 mm
–
14.3
–
420,000
–
PIPER-TQC
100% ( ↑ 2% )
8.1 mm
+34.7%
7.7
+47%
310,000
+26%
FetchSlide
TQC+HER
85%
50.2 mm
–
13.6
–
850,000
–
PIPER-TQC
92% ( ↑ 7% )
20.1 mm
+60.0%
8.3
+39%
680,000
+20%
PickAndPlace
TQC+HER
96%
8.5 mm
–
25.0
–
470,000
–
PIPER-TQC
99% ( ↑ 3% )
4.2 mm
+51.0%
14.6
+42%
362,000
+23%
Table 3: Performance Metrics for Contact-Rich Tasks ( Push, Slide, PickAndPlace ). Comparison between Baseline TQC+HER and PIPER-TQC. Note: Success Rate is included for completeness, but gains are most visible in precision and stability.
Josef Ressel Centre for Intelligent and Secure Industrial Automation, Salzburg University of Applied Sciences, Salzburg, Austria · Paris Lodron University of Salzburg, Salzburg, Austria
the Robert Bosch Center for Cyber-Physical Systems, Indian Institute of Science, Bengaluru. · the Robert Bosch Center for Cyber-Physical Systems and the Department of Computer Science & Automation, Indian Institute of Science, Bengaluru.