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

Biped running can be conceptually reduced to a set of simple and quasi-independent tasks such as weight bearing, upper-body balancing, and energy injection through ankle push-off. We show in this paper that by appropriately designing multi-articular elastic actuators for biped robots in a manner inspired by human biomechanics, these tasks can be favorably expressed in a set of coordinates, in which the system is elastically decoupled. In these coordinates, the robot can be easily controlled by a set of simple and independent control laws. By exploiting the natural dynamics of the specially designed robot, the proposed controller requires only minimal model knowledge (mainly in terms of kinematic and static parameters) and is therefore robust to model uncertainties. It requires only state measurements and no measurement or model based computation of higher order state derivatives. Moreover, since the system is operated at a frequency dictated by the natural resonance, the running gait is energy efficient and resembles to a large extent natural human motion. Simulations validate the concept and demonstrate the independence of the approach from the knowledge of dynamics parameters.

This paper derives a stability statement for a novel, switching based limit cycle control. The stability proof is based on multiple Lyapunov functions and a new interpretation of contraction analysis. By showing that the dissipated energy on the cycle increases with increasing velocity, while the injected energy is constant, the emergence of an attractive limit cycle is shown. The approach applies for general, nonlinear, and compliantly actuated secondorder systems, with positive definite plant parameters and non-aperiodic solutions. An analysis of the controller parameters reveals, that for the majority of parameters, global attractiveness of the limit cycle can be guaranteed. 1 Videos showing applications of the switching based limit cycle control can be found at www.robotic.dlr.de/index.php?id=357 .

There are multiple indications that the nervous system of animals tunes muscle output to exploit natural dynamics of the elastic locomotor system and the environment. This is an advantageous strategy especially in fast periodic movements, since the elastic elements store energy and increase energy efficiency and movement speed. Experimental evidence suggests that coordination among joints involves proprioceptive input and neuromodulatory influence originating in the brain stem. However, the neural strategies underlying the coordination of fast periodic movements remain poorly understood. Based on robotics control theory, we suggest that the nervous system implements a mechanism to accomplish coordination between joints by a linear coordinate transformation from the multi-dimensional space representing proprioceptive input at the joint level into a one-dimensional controller space. In this one-dimensional subspace, the movements of a whole limb can be driven by a single oscillating unit as simple as a reflex interneuron. The output of the oscillating unit is transformed back to joint space via the same transformation. The transformation weights correspond to the dominant principal component of the movement. In this study, we propose a biologically plausible neural network to exemplify that the central nervous system (CNS) may encode our controller design. Using theoretical considerations and computer simulations, we demonstrate that spike-timing-dependent plasticity (STDP) for the input mapping and serotonergic neuromodulation for the output mapping can extract the dominant principal component of sensory signals. Our simulations show that our network can reliably control mechanical systems of different complexity and increase the energy efficiency of ongoing cyclic movements. The proposed network is simple and consistent with previous biologic experiments. Thus, our controller could serve as a candidate to describe the neural control of fast, energy-efficient, periodic movements involving multiple coupled joints.