Alexandre Girard

Alexandre Girard

The answer to the question posed in the title is yes if the context (the list of variables defining the motion control problem) is dimensionally similar. This article explores the use of the Buckingham $π$ theorem as a tool to encode the control policies of physical systems into a more generic form of knowledge that can be reused in various situations. This approach can be interpreted as enforcing invariance to the scaling of the fundamental units in an algorithm learning a control policy. First, we show, by restating the solution to a motion control problem using dimensionless variables, that (1) the policy mapping involves a reduced number of parameters and (2) control policies generated numerically for a specific system can be transferred exactly to a subset of dimensionally similar systems by scaling the input and output variables appropriately. Those two generic theoretical results are then demonstrated, with numerically generated optimal controllers, for the classic motion control problem of swinging up a torque-limited inverted pendulum and positioning a vehicle in slippery conditions. We also discuss the concept of regime, a region in the space of context variables, that can help to relax the similarity condition. Furthermore, we discuss how applying dimensional scaling of the input and output of a context-specific black-box policy is equivalent to substituting new system parameters in an analytical equation under some conditions, using a linear quadratic regulator (LQR) and a computed torque controller as examples. It remains to be seen how practical this approach can be to generalize policies for more complex high-dimensional problems, but the early results show that it is a promising transfer learning tool for numerical approaches like dynamic programming and reinforcement learning.

Francisco Pascoa, Ian Lalonde, Alexandre Girard

Reinforcement learning (RL) policies often fail to generalize to new robots, tasks, or environments with different physical parameters, a challenge that limits their real-world applicability. This paper presents a simple, zero-shot transfer method based on Buckingham's Pi Theorem to address this limitation. The method adapts a pre-trained policy to new system contexts by scaling its inputs (observations) and outputs (actions) through a dimensionless space, requiring no retraining. The approach is evaluated against a naive transfer baseline across three environments of increasing complexity: a simulated pendulum, a physical pendulum for sim-to-real validation, and the high-dimensional HalfCheetah. Results demonstrate that the scaled transfer exhibits no loss of performance on dynamically similar contexts. Furthermore, on non-similar contexts, the scaled policy consistently outperforms the naive transfer, significantly expanding the volume of contexts where the original policy remains effective. These findings demonstrate that dimensional analysis provides a powerful and practical tool to enhance the robustness and generalization of RL policies.

Alexandre Girard, Steven A. Parkison, Philippe Hamelin

Drones can inspect overhead power lines while they remain energized, significantly simplifying the inspection process. However, localizing a drone relative to all conductors using an onboard LiDAR sensor presents several challenges: (1) conductors provide minimal surface for LiDAR beams limiting the number of conductor points in a scan, (2) not all conductors are consistently detected, and (3) distinguishing LiDAR points corresponding to conductors from other objects, such as trees and pylons, is difficult. This paper proposes an estimation approach that minimizes the error between LiDAR measurements and a single geometric model representing the entire conductor array, rather than tracking individual conductors separately. Experimental results, using data from a power line drone inspection, demonstrate that this method achieves accurate tracking, with a solver converging under 50 ms per frame, even in the presence of partial observations, noise, and outliers. A sensitivity analysis shows that the estimation approach can tolerate up to twice as many outlier points as valid conductors measurements.