Energy-based state-feedback control of systems with mechanical or virtual springs

In the last years the classical optimal control of rigid structures gives way to alternatives both in hardware (elastic structures) as in software (non-linear control). In this work we consider both alternatives together. We test the possibility to apply speed-gradient (SG) control [1] to elastic structures. The SG method has many advantages, e.g. exploitation of natural dynamics of the system and mathematically provable criteria of goal achievement. However the cost function that satisfies the requirements of the SG method may be difficult to find. In this work we propose two approaches to this problem: usage of virtual springs and usage of learning methods based on Slow Feature Analysis (SFA). A classical example of a cart-pole system and an example of a system which uses two serial springs for hopping show in simulation the viability of our approach. Proposed here combination of SG control with learning is a novel approach which opens interesting perspectives for further research on passive control.