  We present efficient reduced basis (RB) methods for the simulation of the
coupled problem consisting of a rigid robot hand interacting with soft tissue
material which is modeled by the linear elasticity equation and discretized
with the Finite Element Method. We look at two different scenarios: (i) the
forward simulation and (ii) a feedback control formulation of the model. In
both cases, large-scale systems of equations appear, which need to be solved in
real-time. This is essential in practice for the implementation in a real
robot. For the feedback-scenario, in the context of the linear quadratic
regulator, we encounter a high-dimensional Algebraic Riccati Equation (ARE). To
overcome the real-time constraint by significantly reducing the computational
complexity, we use several structure-preserving and non-structure-preserving
reduction methods. These include proper orthogonal decomposition-based reduced
basis techniques. For the ARE, instead of solving a full dimensional problem we
compute a low-rank-factor and hence a low-dimensional ARE is solved. Numerical
examples for both cases are provided. These illustrate the approximation
quality of the reduced solution and speedup factors of the different reduction
approaches.
