Soft Robotics By Integrating Structure, Materials, Fluids, Control Design, and Signal Processing Using the Tensegrity Paradigm

We should give the soul of soft robotics by enlarging the concepts of structure design, material science, fluid mechanics, and control theory to embrace the more noble task of system design. By system design, we refer to design the components that make up the system, given only the requirements of the overall system. The fundamental challenge is to create theories of system modeling. The existing design approaches deal with what is sufficient rather than necessary, locked into the classical thinking of component technology. That is, design the structure first, followed by material studies and fluid analysis, and add control and signal processing later. The critical question that we should ask is that whether dramatic performance improvements are possible by combining different disciplines as a communal pool of resources such that engineers in different disciplines have more freedom and can talk to each other in design space to solve a joint optimization problem. This dissertation studies the approaches to the system design of soft robotics by integrating structure, materials, fluids, control design, and signal processing using the tensegrity paradigm. Biological systems perhaps provide the greatest evidence that tensegrity is the most efficient structure. Thus, the tensegrity paradigm is chosen for this study. In this dissertation, we first developed the tensegrity structure minimal mass design methods by nonlinear optimizations. This approach allows one to design any solid or hollow bar tensegrity structures with any given external forces (w/o gravity) subject to the structure equilibrium conditions and the maximum stress constraints of structure members (strings yield, bars yield or buckle). Secondly, the tensegrity system dynamics in fluids are derived and studied in two aspects: 1). Tensegrity structures interface fluid directly. Both Class-1 and Class-k tensegrity dynamics with fluid forces incorporated are formulated. 2). Tensegrity structures interface fluid by a skin (membrane) on the structure. The fluid forces are transferred to the structure by the skin on the tensegrity structure. The algorithms enable our ability to perform Fluid-Structure Interaction (FSI) studies of any fluid-based (underwater or in the air) tensegrity structures. Thirdly, general tensegrity dynamics equations based on the Finite Element Method (FEM) and the Lagrangian method with nodal coordinate vectors as the generalized coordinates are presented. This approach allows one to perform nonlinear dynamics, linearized dynamics, and modal analysis of any tensegrity structures with elastic or plastic deformations subject to any boundary constraints. Then, to achieve shape control of tensegrity robots, a nonlinear model-based control law is derived. The control variables (force densities in strings) appear linearly in the nonlinear control. To demonstrate the control performance, we demonstrated a shape controllable tensegrity airfoil, whose topology is based on shape accuracy. This method is suitable for the control of any other tensegrity robots. Finally, a systematic design approach to integrating the sensor/actuator selection (SAS) and covariance control design for tensegrity robots are also studied. The SAS method and the feedback control law problem are converted into an equivalent convex problem, given by a set of LMIs (linear matrix inequalities). The principles can be used to guide sensor and actuator selections, analyze the system performance, and work as an interface to integrate structure, control, and signal processing designs. The theories developed in this dissertation include but are not limited to tensegrity structures