Probabilistic Modeling and Bayesian Filtering for Improved State Estimation for Soft Robots

State estimation is one of the key requirements in robot control, which has been achieved by kinematic and dynamic models combined with motion sensors in traditional robotics. However, it is challenging to acquire accurate proprioceptive information in soft robots due to relatively high noise levels and hysteretic responses of soft actuators and sensors. In this article, we propose a method of estimating real-time states of soft robots by filtering noisy output signals and including hysteresis in the models using a Bayesian network. This approach is useful in constructing a state observer for soft robot control when both the kinematic model of the actuator and the model of the sensor are used. In our method, we regard a hysteresis function as a conditional random process model. We then introduce a dynamic Bayesian network composed of the actuator and the sensor models of the target system using distribution hysteresis mapping. Finally, we show that solving a Bayesian filtering problem is equivalent to suboptimal state estimation of the soft system. This article describes two ways for defining modeling and filtering; one is by Gaussian process regression combined with an extended Kalman filter, and the other is based on variational inference with a particle filter. While the first approach relaxes the uncertainty level in modeling to Gaussian, the second approach illustrates a general probability distribution. We experimentally validate the proposed methods through real-time state estimation of a sensor-integrated soft robotic gripper. The result shows significant improvement in state estimation compared to conventional estimation methods.