Kinematics Computing for Soft Robots: Method based on Geometric Computing and Machine Learning

Soft robots that are built from materials with mechanical properties similar to those of living tissues can achieve tasks like never before in comparison to conventional rigid robots. Powered by the compliance of soft materials and novel structure designs, complex motion (e.g., bending, twisting, and extension) can be accomplished in robotic bodies. We now see soft robots being used to grasp fragile objects and detect confined areas. However, conventional modeling and control approaches, which rely on the rigidity of the robot body, are less effective when directly applied to soft robotic systems. Therefore, new methods and algorithms need to be developed that allow modeling and kinematics control for soft robots.

In model-based robot control, kinematics comprise the fundamental knowledge that can be used to build the mathematical connection between control parameters and robot status. Unlike rigid robots, whose kinematics are well studied and have fast (analytical) solutions, effective and general kinematics computing methods for soft robot systems are still lacking. According to the modeling perspective (i.e., forward kinematics (FK)), predicting the whole-body shape of soft robots under actuation is a non-trivial task since the non-linear deformation in robot bodies and the hyperplastic properties of soft materials create challenges in balancing accuracy and computational costs in existing FK models. The lack of modeling tools further brings the difficulties in developing advanced algorithms to inverse kinematics (IK) and (statics) control thereafter. This Ph.D. project aims to develop a general soft robot kinematics computing pipeline, that can contribute to the effective control of soft robot systems to accomplish given tasks.

A fast numerical simulator for soft robots is firstly presented in this thesis, in which the shape of the robot body is discretely represented by volumetric elements. The development of this simulator was inspired by the fact that the hard-to-model actuation input (e.g., cable force, pressure, and electronic field) in soft robot systems can be directly modeled or transformed to fit the shape change in actuation elements. An optimization pipeline was built to minimize elastic energy in the body elements and compute the deformed shape with actuation parameters as input. As a general numerical simulator, it supports the modeling of various types of actuation, and the hyperelastic soft material properties are integrated. A fast collision checking and response model was added to predict the behavior of soft robots under robot-robot collisions and robot-environment interactions. The numerical computing process of our simulator shows good convergence, even for soft robots with large (rotational) deformation in their bodies, and can therefore balance the computational cost and model precision. In comparison to commercial \textit{finite element analysis} (FEA) software, this geometry-based simulator demonstrates a 20-fold faster computing speed, and the simulation result can well fit the shape that was captured from the physical setup.

The IK problem of soft robots is defined as computing proper actuation parameters that drive soft robots to accomplish given tasks. In this thesis, task-specific IK objectives (which are mainly geometrically defined) are formulated, and the optimal actuation parameters are detected using gradient-based iteration. Through the developed simulator, the gradients of objective functions are estimated using numerical differences. The sequence of motion can be successfully computed using this IK solver, and its efficiency has been verified in two case studies, which include path-following and object pick-and-place.

For the final stage of this Ph.D. project, the speed and precision of the IK solver are enhanced through machine learning. Fully connected neural networks are invited to fit functions of FK and the Jacobian of IK-related objectives. With the high efficiency in the forward propagation of networks (in analytical form), the gradient-based IK solver can run in real-time. Sim-to-real transfer learning is applied to eliminate the reality gap and make the computed actuation parameters more precise in physical setups. Applying sim-to-real transfer learning can also benefit the efficiency of the data generation process. In our pipeline, massive training data is first generated in a virtual environment using a fast simulator; thereafter, a lightweight network layer is employed to map the result of the simulation to the physical hardware. As a result, the amount of physical data can be reduced by 60% to train a network that accurately computes IK solutions.

In conclusion, this dissertation presents a pipeline that computes kinematics solutions for soft robots. A fast geometry-based simulator is presented to contribute to building an iteration-based numerical IK solver. Machine learning is applied to accelerate IK computing to real-time speed with enhanced precision. Task-specific kinematics control is realized in different soft robot systems to verify the effectiveness of the proposed method. The algorithms and code presented in this Ph.D. thesis are open-sourced for researchers and designers, and have the potential to become a general tool for designing and controlling soft robots. Future studies on the design optimization and high-level control of soft robots can all benefit from the research outcomes of this project.