As robots shift from industrial to human-centered spaces, adopting mobile manipulators, which expand workspace capabilities, becomes crucial. In these settings, seamless interaction with humans necessitates compliant control. Two common methods for safe interaction, admittance, and impedance control, require force or torque sensors, often absent in lower-cost or lightweight robots. This paper presents an adaption of impedance control that can be used on current-controlled robots without the use of force or torque sensors and shows its application for compliant control of a mobile manipulator. A calibration method is designed that enables estimation of the actuators’ current/torque ratios and frictions, used by the adapted impedance controller, and that can handle model errors. The calibration method and the performance of the designed controller are experimentally validated using the Kinova GEN3 Lite arm. Results show that the calibration method is consistent and that the designed controller for the arm is compliant while also being able to track targets with five-millimeter precision when no interaction is present. Additionally, this paper presents two operational modes for interacting with the mobile manipulator: one for guiding the robot around the workspace through interacting with the arm and another for executing a tracking task, both maintaining compliance to external forces. These operational modes were tested in real-world experiments, affirming their practical applicability and effectiveness.Code: https://github.com/tud-amr/mobile-manipulator-compliance

At first glance, a floating-base robotic system is a kinematic chain, and its equations of motion are described by the inertia-coupled dynamics of its shape and movable base. However, the dynamics embody an additional structure due to the momentum evolution, which acts as a velocity constraint. In prior works of robot dynamics, matrix transformations of the dynamics revealed a block-diagonal inertia. However, the structure of the transformed matrix of Coriolis/Centrifugal (CC) terms was not examined, and is the primary contribution of this article. To this end, we simplify the CC terms from robot dynamics and derive the analogous terms from geometric mechanics. Using this interdisciplinary link, we derive a two-part structure of the CC matrix, in which each partition is iteratively computed using a self-evident velocity dependency. Through this CC matrix, we reveal a commutative property, the velocity dependencies of the skew-symmetry property, the invariance of the shape dynamics to the basis of momentum, and the curvature as a matrix operator. Finally, we show the application of the proposed CC matrix structure through controller design and locomotion analysis.

In this contribution the problem of vibration control is studied on the basis of a fundamental oscillatory system consisting of a mass spring system and an additional mass. The proposed control strategy couples the orbits of the two masses such that both masses stop, while simultaneously stabilizing the second mass to a desired equilibrium. Using a coordinate and input transformation, the control strategy is directly transferred to an n-link manipulator mounted on a base with linear translational stiffness. Using semidefinite Lyapunov functions and a conditional stability argument, it is shown that the proposed control strategy damps out base vibrations, while additionally achieving a desired configuration in the task-space. Finally, the proposed method is compared to a state-of-the-art approach using numerical simulations.

Interactions between robots and their environment give rise to external wrenches acting on the robot structure. The estimation of the resulting torques in the joints is fundamental in human-robot interaction to detect/identify collisions and perform suitable reaction strategies. Other applications may require to use the estimation for compensating the effects of the external torques within the control loop. The well-established momentum observer, which relies on proprioceptive sensors only, is usually used for these purposes. In this work, the momentum dynamics is used to derive new observers. While the classic momentum observer provides a first-order filtered version of the external torques, here a (theoretically) finite-time convergence is achieved. Simulations and experiments are used to validate the performance of the proposed methods.

The concept of hybrid zero dynamics is a promising approach for designing exponentially stabilizing controllers for dynamic walking with some degrees of underactuation. By this approach a feedback controller is designed such that a stable periodic orbit, within an invariant submanifold for the hybrid closed-loop system is created. This is usually achieved through an exponentially fast dynamics transverse to the zero dynamics manifold and the stability properties of such periodic orbit is then transferred to the full-order dynamic system. In this paper a passivity-based controller for a planar biped with one degree of underactuation is designed. By this approach we aim to preserve the natural dynamics of the system in the transverse dynamics (i.e. the dynamics transverse to the zero dynamics manifold) in contrast to the common input-output linearization method which cancels these dynamics. A Lyapunov stability analysis of the full-order system based on the conditional stability theorem is presented. By this analysis, the asymptotic stability of the periodic orbit in lower dimensional state space is extended to the full dimensional space. The results of the analysis are verified by simulation on a seven-link biped robot walking with zero ankle torque in sagittal plane.

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.

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.

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.

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.