Human-Robot Kinaesthetic Interaction Based on Free Energy Principle

TL;DR

The paper addresses how human and robot action intentions interact during kinaesthetic joint actions and frames this within the Free Energy Principle using a probabilistic variational RNN (PV-RNN). It trains PV-RNN with a meta-prior $w$ to balance top-down intentions against bottom-up sensory evidence, and tests human-guided transitions with a force-feedback Torobo controller. Key findings show that increasing the interaction-phase meta-prior $w^i$ strengthens the robot's top-down intention, increasing the counter-force needed to induce transitions, while untrained transitions demand more force than trained ones. The work provides a principled link between latent-variable dynamics, free-energy terms, and measurable interaction forces, with implications for designing embodied, cooperative human-robot systems.

Abstract

The current study investigated possible human-robot kinaesthetic interaction using a variational recurrent neural network model, called PV-RNN, which is based on the free energy principle. Our prior robotic studies using PV-RNN showed that the nature of interactions between top-down expectation and bottom-up inference is strongly affected by a parameter, called the meta-prior, which regulates the complexity term in free energy.The study also compares the counter force generated when trained transitions are induced by a human experimenter and when untrained transitions are induced. Our experimental results indicated that (1) the human experimenter needs more/less force to induce trained transitions when $w$ is set with larger/smaller values, (2) the human experimenter needs more force to act on the robot when he attempts to induce untrained as opposed to trained movement pattern transitions. Our analysis of time development of essential variables and values in PV-RNN during bodily interaction clarified the mechanism by which gaps in actional intentions between the human experimenter and the robot can be manifested as reaction forces between them.

Figures (8)

• Figure 1: Graphical representation of the interaction phase of PV-RNN. $d_{l, t}, z^p_{l, t}, z^q_{l, t}, x_{t}$ and $\Bar{x}_{t}$ indicates the deterministic latent variable, prior distribution, approximate posterior, output and target of layer $l$ and time-step $t$, respectively. Blue and red arrows indicate forward propagation and backward propagation, respectively. The future, the past within the window and the past outside the window are coloured red, blue, and green respectively. The past window size is 2 in this graphical model. a) shows the network at time-step $t$. b) shows the network at time-step $t+1$.
• Figure 2: the human interacting with Torobo, the PV-RNN target joint angle generator, the inverse model, and the PID joint controller.
• Figure 3: Schematic of the probabilistic finite state machine from which training data was generated.
• Figure 4: Resultant time-development from the training phase of one of the PV-RNN models. Development of KLD with respect to the number of training epochs is shown for (a) the Top layer (layer 2) and (b) the Bottom layer (layer 1). Development of the average prediction error over time steps in each teaching sequence is shown in (c).
• Figure 5: Time-development of excess torque, prediction error, and KL-divergence between the approximate posterior and the prior in trained movement transitions in cases with three different meta-prior $w^i$ settings with $0.01$, $0.05$, and $0.1$. The grey area represents the past window where the head of the window is the current time. The window is shifted 5 times during the movement transition AB.