Physical compliance can be considered one of the key technical properties a robot should exhibit to increase its mechanical robustness. In addition, the accompanying temporal energy storing capabilities enable explosive and energy efficient cyclic motions. But these advantages come at a price, as compliance introduces unwanted intrinsic oscillatory dynamics, underactuation, and reduces the natural frequency of the plant. These aspects make control of the link configuration variables a challenging task. This work presents two novel control methods for implementing link-side motion tracking capabilities and injecting a desired damping characteristic to suppress link vibrations along the reference trajectory for compliantly actuated robots with nonlinear elastic characteristics. We prove their uniform global asymptotic stability by invoking a theorem by Matrosov. Both approaches, namely ESP and ESP+, have in common that they preserve the link-side inertial properties and the elastic structure of the original plant dynamics, hence the name Elastic Structure Preserving control. Apart from that, ESP control focuses on preserving the inertial properties of motor dynamics. While ESP+ control aims at minimizing the dynamic shaping on the motor side. The performance of the feedback control laws have been evaluated on the variable stiffness robot arm DLR Hand Arm System, where the stiffness in each of its joints is highly nonlinear. To the best of our knowledge, this is the first experimentally validated tracking controller for compliantly actuated, multi-joint robots with nonlinear elastic elements.

Compliant actuators in robotic systems improve robustness against rigid impacts and increase the performance and efficiency of periodic motions such as hitting, jumping and running. However, in the case of rigid impacts, as they can occur during hitting or running, the system behavior is changed compared to free motions which turns the control into a challenging task. We introduce a controller that excites periodic motions along the direction of an intrinsic mechanical oscillation mode. The controller requires no model knowledge and adapts to a modal excitation by means of measurement of the states. We experimentally show that the controller is able to stabilize a hitting motion on the variable stiffness robot DLR Hand Arm System. Further, we demonstrate by simulation that the approach applies for legged robotic systems with compliantly actuated joints. The controlled system can approach different modes of motion such as jumping, hopping and running, and thereby, it is able to handle the repeated occurrence of robot-ground contacts.

The elastic energy storages in biologically inspired Variable Impedance Actuators (VIA) offer the capability to execute cyclic and/or explosive multi degree of freedom (DoF) motions efficiently. This paper studies the generation of cyclic motions for strongly nonlinear, underactuated multi DoF serial robotic arms. By experimental observations of human motor control, a simple and robust control law is deduced. This controller achieves intrinsic oscillatory motions by switching the motor position triggered by a joint torque threshold. Using the derived controller, the oscillatory behavior of human and robotic arms is analyzed in simulations and experiments. It is found that the existence of easily excitable oscillation modes strongly depends on the damping properties of the plant. If the intrinsic damping properties are such that oscillations excited in the undesired modes decay faster than in the desired mode, then multi-DoF oscillations are easily excitable. Simulations and experiments reveal that serially structured, elastic multi-body systems such as VIA or human arms with approximately equal joint damping, fulfill these requirements.

Biologically inspired Variable Impedance Actuators (VIA) offer the capability to execute cyclic and/or explosive multi degree of freedom (DoF) motions efficiently by storing elastic energy. This paper studies the preconditions which allow to induce robust cyclic motions for strongly nonlinear, underactuated multi DoF robotic arms. By experimental observations of human motor control, a simple control law is deduced. This controller achieves intrinsic oscillatory motions by switching the motor position triggered by a joint torque threshold. Using the derived controller, the periodic behavior of the robotic arm is analyzed in simulations. It is found that a modal analysis of the linearized system at the equilibrium point allows to qualitatively predict the periodic behavior of this type of strongly nonlinear systems. The central statement of this paper is that cyclic motions can be induced easily in VIA systems, if the eigenfrequencies and modal damping values of the linearized system are well separated. Validation is given by simulation and experiments, where a human controls a simulated robotic arm, and the developed regulator controls a robotic arm in simulation and experiments.

Pogo-stick bouncing or the spring loaded inverted pendulum represent fundamental dynamics models for hopping and running in legged locomotion. However, these conceptual models are in general of lower order than the elastic multibody dynamics of versatile segmented legs. The question how to embody these simple models into real robot leg designs still has not been completely answered so far. The concept of eigenmodes for linear systems provides a tool to separate high-dimensional, coupled dynamics in one-dimensional (1-D) invariant ones. However, the dynamics of segmented legs is in general nonlinear such that even the existence of periodic motions, as appearing typically in locomotion tasks, cannot be generally guaranteed without changing intrinsic dynamics behavior substantially by control. This paper extends the concept of eigenmodes, which is well-known for linear systems, to the nonlinear case. By proposing a method for selecting the design parameters of multibody systems such that desired eigenmodes are achieved, the problem of embodying fundamental locomotion modes into legged systems is resolved. Examples of practically realizable leg designs are provided, which proof the existence of invariant, 1-D oscillation modes in nonlinear, elastic robot dynamics. An experiment on a multilegged robotic system validates that energetic efficiency can be gained by the proposed approach. C(q 0 + wz, wż)wż ∂U (q) ∂q T q=q 0 +wz −M (q 0 + wz) −1 −M (q 0 + wz) −1q = wz T ⋆ q 0 +wz T ⋆ q 0