Learning Low-Level Causal Relations using a Simulated Robotic Arm

TL;DR

This work investigates learning and exploiting low-level causal relations in robotic systems using simulated data. By training forward and inverse models on motor-babbling data from a simulated robotic arm and applying SHAP and PDP-based attribution, the authors extract actionable insights about how individual state features (robot joints and environmental objects) causally affect outcomes, enabling dimensionality reduction and explainability. The forward model supports multi-step mental simulation (up to 10 steps), and two inverse-model architectures (monolithic and pre-computation) offer viable pathways for action prediction, with explainability analyses revealing which features matter for specific tasks. The approach promises more robust, explainable planning and imitation-learning–driven control in complex robotic environments, especially where intuitive physics and low-level causal structure drive behavior.

Abstract

Causal learning allows humans to predict the effect of their actions on the known environment and use this knowledge to plan the execution of more complex actions. Such knowledge also captures the behaviour of the environment and can be used for its analysis and the reasoning behind the behaviour. This type of knowledge is also crucial in the design of intelligent robotic systems with common sense. In this paper, we study causal relations by learning the forward and inverse models based on data generated by a simulated robotic arm involved in two sensorimotor tasks. As a next step, we investigate feature attribution methods for the analysis of the forward model, which reveals the low-level causal effects corresponding to individual features of the state vector related to both the arm joints and the environment features. This type of analysis provides solid ground for dimensionality reduction of the state representations, as well as for the aggregation of knowledge towards the explainability of causal effects at higher levels.

Figures (5)

• Figure 1: General forward model architecture. The linear layer denotes a fully connected layer with linear activation; hidden layers are $\tanh$-activated. $\dim(\hbox{$\bm{\cdot}$})$ in the I/O layers designates their size.
• Figure 2: Architectures of monolithic IM and IM with $\bm{\theta}(t+1)$ pre-computation pre-network. The linear layer denotes a fully connected layer with linear activation, and hidden layers with ($\tanh$) are $\tanh$-activated. Multipliers next to some layers (e.g., 4x) denote the number of stacked layers of the same type. $\dim(\hbox{$\bm{\cdot}$})$ in some layers designates their size.
• Figure 3: Average MAE and its standard deviation of joint configuration and effector position prediction by the forward model during mental simulation 10 steps ahead.
• Figure 4: Contribution heat map generated by Deep SHAP method on the forward model showing the magnitude of the contribution of specific actions to output features.
• Figure 5: A sample of partial dependence plots generated by Deep SHAP method applied to the forward model showing correlation between a value of a specific action component and its contribution to an output variable.