Unsupervised Implicit Parameter Estimation of Sensor-Limited Musculoskeletal Robots Using Time-Differentiable Neural Networks

To enable effective trajectory tracking, robot systems usually require an inverse dynamics model (IDM) for feed-forward compensation. However, for pneumatic musculoskeletal robots (PMRs), even if the closed-form expressions of their IDMs are well-established, explicit parameter estimation can still be tough due to the lack of torque and acceleration sensors. Without the necessary devices to provide labeled data, this paper proposes an unsupervised solution to implicitly estimate the dynamics parameters of PMRs. In detail, to overcome the sensor limitation, the IDM of multi-joint PMRs is formulated as a torque-free version and identified online with an acceleration-free strategy. To further handle the influence of actuator dynamics on the IDM, the time-differentiable multi-layer perceptrons are introduced to provide matrix output support and compute the time derivative of the fitting target. The proposed method is called unsupervised since it requires no cost function back-propagation, and its performance is evaluated with two indirect criteria in the absence of ground truth. According to the experiment results on a self-made PMR, even without direct supervision, the estimated parameters can still provide a trustworthy description of the system behavior which is competent for both model-based tracking control and future state prediction. Note to Practitioners - This paper is motivated by the effort to transfer the established motion control strategies in industrial manipulators to pneumatic musculoskeletal robots (PMRs). However, these strategies rely on accurate inverse dynamics models (IDMs), thus conflicting with the limited sensor configuration in PMRs. To address this issue, an unsupervised solution is proposed based on a unique time-differentiable neural network. This method couples the IDM with a model-based controller and enables indirect parameter estimation by optimizing the controller instead. Unlike conventional inverse dynamics learning approaches, our method requires neither torque sensing nor acceleration estimation, making it ideal for low-cost and lightweight devices such as assistive and rehabilitation robots. To further simplify implementation, an equivalent cost function is provided to the readers such that they can quickly deploy our method on their own hardware using the common machine learning frameworks. Among the major steps in IDM identification, this work mainly focuses on the process of parameter estimation and does not address the design of optimal excitation signals, which we plan to explore in future research.