Gianluca Garofalo

Overview of the torque-controlled humanoid robot TORO

This paper gives an overview on the torque-controlled humanoid robot TORO, which has evolved from the former DLR Biped. In particular, we describe its mechanical design and dimensioning, its sensors, electronics and computer hardware. Additionally, we give a short introduction to the walking and multi-contact balancing strategies used for TORO.

Walking control of fully actuated robots based on the Bipedal SLIP model

The goal of this paper is to generate and stabilize a periodic walking motion for a five degrees of freedom planar robot. First of all we will consider a biped version of the spring loaded inverted pendulum (SLIP), which shows openloop stable behavior. Then we will control the robot behavior as close as possible to the simple model. In this way we take advantage of the open-loop stability of the walking pattern related to the SLIP, and additional control actions are used to increase the robustness of the system and reject external disturbances. To this end an upper level controller will deal with the stabilization of the SLIP model, while a lower level controller will map the simple virtual model onto the real robot dynamics. Two different approaches are implemented for the lower level: in the first one, we aim at exactly reproducing the same acceleration that a SLIP would have when put in the same condition, while in the second one, we aim at a simpler control law without exactly reproducing the aforementioned acceleration. The latter case is equivalent to considering a SLIP with additional external disturbances, which have to be handled by the upper level controller. Both approaches can successfully reproduce a periodic walking pattern for the robot.

Orbital stabilization of mechanical systems through semidefinite Lyapunov functions

In this paper we address the problem of generating asymptotically stable limit cycles for a fully actuated multibody mechanical system through a feedback control law. Using the concept of conditional stability the limit cycle can be designed for a lower dimensional dynamical system describing how the original one evolves on a chosen submanifold and the corresponding velocity space. Moreover, the controller can be split up in two parts that can be independently designed and analyzed in order to reach the constraint submanifold and then produce the oscillation. Even if designed assuming a lower dimensional system, the limit cycle implies a periodic motion for the whole system.

On the closed form computation of the dynamic matrices and their differentiations

In this paper we review and extend some classic results on rigid body dynamics, in order to give a symbolic expression of the different derivatives of the matrices of the dynamic model of a general tree-structured robot. In what follows the matrices are differentiated with respect to time, state and dynamic parameters. Obviously from the derivatives of the single matrices it is possible to recover the derivatives of the direct and inverse dynamic functions and classic results like the regressor matrix. Moreover an iterative algorithm is sketched which allows to compute all these derivatives as well as the kinematics and dynamics of the robot.

Modal limit cycle control for variable stiffness actuated robots

This paper presents a control approach to stabilize limit cycle motions along a mechanical mode of variable stiffness actuated (VSA) robots. Thereby, first a PD controller with gravity and Coriolis/centrifugal compensation shapes a desired dynamics, which is decoupled in terms of modal coordinates. Then an asymptotically stable limit cycle is generated on the link side dynamics for a selected mode. Finally, the modal control approach first introduced for rigid robots is extended to the VSA case. This is done by a joint torque controller, which decouples the torque dynamics from the link side dynamics. Stability and convergence are proven for the dynamics resulting from each feedback control. Furthermore, the energy efficiency of the proposed approach is verified by simulation and experiments on the VSA robotic arm DLR Hand Arm System.

Control applications of TORO — A Torque controlled humanoid robot

Summary form only given: This video presents an overview of the hardware and control applications of the TOrque-controlled humanoid RObot TORO developed at DLR. The self-contained robot was developed as a research platform for walking and whole-body control. It is based on the drive units of the DLR-KUKA Lightweight Robot Arm (LBR) III, has a total of 39 DoF, and it can be operated both in position and torque control modes. The internal state of the robot can be measured by the motor position and torque sensors, plus two IMUs in the trunk and head. Force/torque sensors at the ankles provide measurements to evaluate the stability of the robot, and stereo cameras plus one RGB-D sensor are integrated in the head for research on autonomous navigation and manipulation. The integrated joint torque sensors allow a highly sensitive inner loop joint torque control. Based on torque control different impedance behaviors can be easily realized, which is demonstrated by an energy-based limit cycle controller used in a simple hand-shaking demonstration. The walking controller is based on the Divergent Component of Motion (DCM), also known as Capture Point. Reference trajectories for the DCM, which correspond to ZMP trajectories on the robot feet, are generated and tracked by a feedback control. The high level walking commands for the robot can be autonomously generated or can be introduced via a proportional velocity input from a gaming console remote control. A multi-contact whole-body controller for balancing and posture stabilization is implemented using optimization of contact wrenches and is tested in different contact situations.

Jumping Control for Compliantly Actuated Multilegged Robots

A feedback control to generate jumping motions for compliantly actuated multilegged robots is proposed. The method allows to specify the direction of the jumping motion. This is achieved by a constraint that defines a one-dimensional submanifold and a bang-bang control which generates a limit cycle on this submanifold. The approach is based on classical impedance control with the difference that the stiffness on the submanifold and the force to preserve a predefined nominal body configuration result from the intrinsic mechanical springs in the joints. Furthermore, we propose two controller implementations: the first implementation does not require to detect the contact state, while the second implementation requires contact state detection, but accounts in addition for Coulomb friction constraints. The controller is validated in simulation with a compliantly actuated quadruped.

Limit Cycle Control Using Energy Function Regulation With Friction Compensation

In this letter, we consider the problem of generating periodic solutions for fully actuated robots with unknown disturbances, which can be modeled using a regressor matrix. We extend our previous work on limit cycle control based on energy function regulation for the case when disturbance torques are acting on the system, e.g., torques due to friction. Since the controller is designed in two independent steps, the compensation of the friction cannot be carried on with standard techniques and it will be split in two steps as well. In the first one, we reduce the dimension of the dynamical system and use a sliding mode approach for friction compensation, and in the second, we produce the desired limit cycle and use an adaptive approach for friction compensation. Crucial for the analysis is the concept of conditional attractiveness with semidefinite Lyapunov functions, that we formulate in letter to show the attractiveness of a closed orbit of the whole system, even if it is designed assuming a reduced dynamics. Finally, we validate our approach with experiments on a humanoid robot.

On the regulation of the energy of elastic joint robots: Excitation and damping of oscillations

The paper presents a new control law for elastic joint robots that allows to regulate the energy stored in the system to a desired value. Being able to either remove energy from the system or inject it, oscillations can be both damped out and induced. Therefore the control law can be used for asymptotic regulation to a desired configuration and (in case of additional constraints) generation of asymptotically stable limit cycles. Compared to other methods, we can formally guarantee the previous property keeping at the same time the control law simple and easy to implement. Furthermore, using the energy stored by the intrinsic elastic elements in the joints, high energy efficiency is achieved. Simulations and experiments are also provided, in order to further validate the theoretical results.

Energy Based Limit Cycle Control of Elastically Actuated Robots

A new control law for elastic joint robots that allows to regulate an energy function of the system to a desired value is presented in this technical note. Being able to either remove energy from the system or inject into it, oscillations can be both damped out and induced. The proposed nonlinear dynamic state feedback controller forces the system to evolve on a submanifold of the configuration space. The reduced dynamics of the system and of the controller itself are similar to a single elastic joint, for which an asymptotically stable limit cycle is obtained regulating an energy function to a positive desired value. When the desired value of the energy function is chosen to be zero, then the asymptotically stable limit cycle reduces to an asymptotically stable equilibrium point. In this case the oscillations are damped out and the desired task-space configuration is reached. The design of the controller extensively uses the concept of conditional stability, so that the limit cycle can be designed for a lower dimensional dynamical system, although it will result to be a limit cycle for the whole system.