One of the essential aspects of humanoid robot running is determining the limb-swinging trajectories. During the flight phases, where the ground reaction forces are not available for regulation, the limb swinging trajectories are significant for the stability of the next stance phase. Due to the conservation of angular momentum, improper leg and arm swinging results in highly tilted and unsustainable body configurations at the next stance phase landing. In such cases, the robotic system fails to maintain locomotion independent of the stability of the center of mass trajectories. This problem is more apparent for fast and high flight time trajectories. This paper proposes a real-time nonlinear limb trajectory optimization problem for humanoid running. The optimization problem is tested on two different humanoid robot models, and the generated trajectories are verified using a running algorithm for both robots in a simulation environment.

In this work, we present a novel control approach based on partial feedback linearization (PFL) for the stabilization of a suspended aerial platform with an attached load. Such systems are envisioned for various applications in construction sites involving cranes, such as the holding and transportation of heavy objects. Our proposed control approach considers the underactuation of the whole system while utilizing its coupled dynamics for stabilization. We demonstrate using numerical stability analysis that these coupled terms are crucial for the stabilization of the complete system. We also carried out robustness analysis of the proposed approach in the presence of external wind disturbances, sensor noise, and uncertainties in system dynamics. As our envisioned target application involves cranes in outdoor construction sites, our control approaches rely on only onboard sensors, thus making it suitable for such applications. We carried out extensive simulation studies and experimental tests to validate our proposed control approach.

This paper studies the experimental comparison of two different whole-body control formulations for humanoid robots: inverse dynamics whole-body control (ID-WBC) and passivity-based whole-body control (PB-WBC). The two controllers fundamentally differ from each other as the first is formulated in task acceleration space and the latter is in task force space with passivity considerations. Even though both control methods predict stability under ideal conditions in closed-loop dynamics, their robustness against joint friction, sensor noise, unmodeled external disturbances, and non-perfect contact conditions is not evident. Therefore, we analyze and experimentally compare the two controllers on a humanoid robot platform through swing foot position and orientation control, squatting with and without unmodeled additional weights, and jumping. We also relate the observed performance and characteristic differences with the controller formulations and highlight each controller’s advantages and disadvantages.

Suspended multirotor platforms are fascinating systems that can be employed in construction applications to provide safe transportation of heavy loads. Such a system comprising a cable-suspended platform with attached load features seven degrees of freedom (DoF) motion for the whole system. In this paper, we propose a composite whole-body control framework for the stabilization of the suspended multirotor platform system, leveraging singular perturbation theory to exploit the inherent three time-scale dynamics of the system. The control strategy computes the underactuated 3-DoF wrench space generated by the platform’s actuation units for the stabilization of the complete system. Building upon this, we develop a superposition-based shared control approach and then compare the two controllers. Moreover, to address specific cases where the time-scale separation between two dynamics of the triple-spherical pendulum becomes negligible, we design an operational space controller. The control approaches are validated using both extensive numerical simulations and experiments in different scenarios. We also carried out numerical robustness and stability analysis of the whole system. Note that our system relies on only onboard sensors for state estimation, which makes it effective for real-life outdoor applications.

In this work, we present a novel actuation strategy for a suspended aerial platform. By utilizing an underactuation approach, we demonstrate the successful oscillation damping of the proposed platform, modeled as a spherical double pendulum. A state estimator is designed in order to obtain the deflection angles of the platform, which uses only onboard IMU measurements. The state estimator is an extended Kalman filter (EKF) with intermittent measurements obtained at different frequencies. An optimal state feedback controller and a PD+ controller are designed in order to dampen the oscillations of the platform in the joint space and task space respectively. The proposed underactuated platform is found to be more energy-efficient than an omnidirectional platform and requires fewer actuators. The effectiveness of our proposed system is validated using both simulations and experimental studies.

This article introduces a framework for complex human-robot collaboration tasks, such as the co-manufacturing of furniture. For these tasks, it is essential to encode tasks from human demonstration and reproduce these skills in a compliant and safe manner. Therefore, two key components are addressed in this work: motion generation and shared autonomy. We propose a motion generator based on a time-invariant potential field, capable of encoding wrench profiles, complex and closed-loop trajectories, and additionally incorporates obstacle avoidance. Additionally, the paper addresses shared autonomy (SA) which enables synergetic collaboration between human operators and robots by dynamically allocating authority. Variable impedance control (VIC) and force control are employed, where impedance and wrench are adapted based on the human-robot autonomy factor derived from interaction forces. System passivity is ensured by an energy-tank based task passivation strategy. The framework’s efficacy is validated through simulations and an experimental study employing a Franka Emika Research 3 robot.

During operation, aerial manipulation systems are affected by various disturbances. Among them is a gravitational torque caused by the weight of the robotic arm. Common propeller-based actuation is ineffective against such disturbances because of possible overheating and high power consumption. To overcome this issue, in this paper we propose a winch-based actuation for the crane-stationed cable-suspended aerial manipulator. Three winch-controlled suspension rigging cables produce a desired cable tension distribution to generate a wrench that reduces the effect of gravitational torque. In order to coordinate the robotic arm and the winch-based actuation, a model-based hierarchical whole-body controller is adapted. It resolves two tasks: keeping the robotic arm end-effector at the desired pose and shifting the system center of mass in the location with zero gravitational torque. The performance of the introduced actuation system as well as control strategy is validated through experimental studies.

The on-ground validation of orbital manipulators is a challenging task because the robot is designed for a gravity-free operational environment, but it is validated under the effect of gravity. As a consequence, joint torque limits can be easily reached in certain configurations when gravity is actively compensated by the joints. Hence, the workspace for on-ground testing is restricted. In this paper, an optimal strategy is proposed for achieving gravity compensation of an orbital manipulator arm on ground. The strategy minimizes the joint torques acting on the manipulator by solving an optimization problem and it computes the necessary forces to be tracked by an external carrier. Hence, full gravity compensation is achieved for the orbital manipulator. Experimental results validate the effectiveness of the method on the DLR CAESAR space robot, which uses a cable suspended system as external carrier to track the desired gravity compensation force, resulting from the proposed method.

Hardware-in-the-loop simulation (HILS) allows a more realistic evaluation of control approaches than what is possible with pure software simulations, but without the actual complexity of the complete system. This is important for some complex systems such as orbital robots, where testing of the system is typically not possible after its launch, and an on-ground replica is used to validate the performance of such a system. In this article, an impedance-matching approach is presented to match the end-effector dynamics of a fixed-base robot manipulator with that of a target vehicle-manipulator system (VMS), while taking into account the redundant nullspace dynamics in a connected real-time simulation framework. This approach ensures that the forces and torques exerted by the system on the environment matches with that of the simulated system. The contact wrenches used in our approach are not obtained from numerical simulations, but rather from real physical interaction, which is one of the main advantages of our approach. The effectiveness of our method is validated by demonstrating various physical interaction tasks with the environment, using a suspended aerial manipulator as the target system.

This study extends the whole-body control (WBC) formulation for bipedal humanoid robots that include closed (parallel) kinematic chains in their structure. Along with general formulation, we also stress the implementation of this formulation on Kangaroo, which is a highly dynamic humanoid robot developed by PAL Robotics. This 76-DOF robot includes 24 independent closed-kinematic chains in its structure and constitutes a good case study for our approach. We discuss the WBC formulation for various control structures, including inverse dynamics control (IDC) and Modular Passive Tracking Control (MPTC). As a test scenario, we employ a 3D spring-loaded inverted pendulum (SLIP) jumping trajectory with disturbance rejection as the desired CoM trajectory.

Running and jumping are locomotion modes that allow legged robots to rapidly traverse great distances and overcome difficult terrain. In this article, we show that the 3-D divergent component of motion (3D-DCM) framework, which was successfully used for generating walking trajectories in previous works, retains its validity and coherence during flight phases, and, therefore, can be used for planning running and jumping motions. We propose a highly efficient motion planner that generates stable center-of-mass (CoM) trajectories for running and jumping with arbitrary contact sequences and time parametrizations. The proposed planner constructs the complete motion plan as a sequence of motion phases that can be of different types: stance, flight, transition phases, etc. We introduce a unified formulation of the CoM and DCM waypoints at the start and end of each motion phase, which makes the framework extensible and enables the efficient waypoint computation in matrix and algorithmic form. The feasibility of the generated reference trajectories is demonstrated by extensive whole-body simulations with the humanoid robot TORO.

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.

This paper proposes a parameterization method to represent SO (3) over multiple turns. This method is called a memory-based parameterization, because the idea is to integrate the past trajectory of exponential coordinates. The parameterization is consistent in the sense that the true rotation matrix can be reconstructed by using the exponential map. As an application of the proposed method, a 6D impedance controller is designed with a radially unbounded potential function. Consequently, in contrast to the conventional methods, an arbitrarily large angular deflection can be accommodated, resulting in a more realistic impedance behavior. The proposed schemes are validated through simulations and experiments.

Embedding elastic elements into legged robots through mechanical design enables highly efficient oscillating patterns that resemble natural gaits. However, current trajectory planning techniques miss the opportunity of taking advantage of these natural motions. This work proposes a locomotion planning method that aims to unify traditional trajectory generation with modal oscillations. Our method utilizes task-space linearized modes for generating center of mass trajectories on the sagittal plane. We then use nonlinear optimization to find the gait timings that match these trajectories within the Divergent Component of Motion planning framework. This way, we can robustly translate the modes-aware centroidal motions into joint coordinates. We validate our approach with promising results and insights through experiments on a compliant quadrupedal robot.

Gait generation frameworks for humanoid robots typically assume a constant centroidal angular momentum (CAM) throughout the walking cycle, which induces undesirable contact torques in the feet and results in performance degradation. In this work, we present a novel algorithm to learn the CAM online and include the obtained knowledge within the closed-form solutions of the Divergent Component of Motion (DCM) locomotion framework. To ensure a reduction of the contact torques at the desired center of pressure position, a CAM trajectory is generated and explicitly tracked by a whole-body controller. Experiments with the humanoid robot TORO demonstrate that the proposed method significantly increases the maximum step length and walking speed during locomotion.

In this paper, we propose a detumbling strategy that stabilizes the motion of a tumbling client satellite using an orbital servicing manipulator, which is the goal of the post-grasp phase. One of the critical aspects in this phase is ensuring that excessive contact forces are not generated at the grasp interface. In addition, space mission requirements might demand a nominal manipulator configuration that is suitable for further manipulation/servicing activities. The proposed strategy allows the detumbling of the client motion while ensuring that the contact forces developed at the grasp interface do not violate a safety threshold. Further, it allows the reconfiguration of the manipulator arm by exploiting the full actuation capability of the manipulator-equipped servicing spacecraft. The controller guarantees joint task convergence in the nullspace of the manipulator's end-effector, and is also valid for kinematically singular configurations of the manipulator. It is further augmented using a quadratic programming based approach to optimally constrain the contact forces. Finally, simulation results for a post-grasp detumbling scenario are shown to validate the effectiveness of the proposed method.

This article presents passive impedance control of flexible joint robots (FJRs) via inner-loop torque control of elastic joints. However, according to our theoretical analysis, the torque control methods of series elastic actuators (SEAs) are often limited by the fact that the acceleration signals are amplified by the control gains. Since the acceleration signals are often affected by differentiation noise, the analysis may become invalid in practice. To alleviate this limitation, we propose the use of the so-called series viscoelastic actuator (SvEA), which significantly reduces the acceleration amplification. Consequently, in contrast to the SEA case, the theoretical analysis of an SvEA-based FJR is valid in real implementations. We would like to highlight the fact that the theoretical analysis (more specifically, passivity analysis) is performed for nonlinear robot dynamics without linearization. As a result, the passive impedance controller can be realized more robustly with enhanced inner-loop torque control.

This article presents a hierarchical passivity-based compliance controller that exploits robot redundancy and aims at achieving an impedance behavior with a time-varying stiffness on all the priority levels. Unfortunately, this gives rise to certain control actions that lead to the loss of the safety-critical passivity feature. To deal with this problem, we employ the concept of virtualenergy tanksthat keep track of the passivity violating energy in the system, ensuring that it remains bounded. This restores the passivity in the system, which guarantees the stable interaction with any passive environment. Furthermore, we augment our controller with an additional safety layer, which ensures that the energy injected through the tank into the system remains below a safe limit, defined based on the maximum kinetic energy allowed in the system. Finally, our approach is validated in terms of performance during task execution and safety both in simulations and on real-robot hardware.

Multi-agent control of a robot using multiple controllers is vital in domains like shared control and reliable control. The strategy of assigning a varying priority (authority) to each agent controller, and commanding the robot using an authority-weighted sum of the forces produced by all the agents has been exploited in prior works. In this paper, firstly, we show that this strategy results in a loss of passivity, and we identify the passivity-disrupting scaling-related terms. Secondly, we propose a model independent method to ensure finite-gain L2stability of such a generic multi-agent robot control system with time-varying force scaling factors. Thirdly, the analysis is validated with simulations and hardware experiments.

In this paper, we present a highly efficient Divergent Component of Motion (DCM) reference trajectory generator capable of adapting online to large perturbations acting on the center-of-mass (push recovery) and on the swing foot (stumble recovery). For push recovery, we propose an analytic solution for a footstep adjustment strategy based on the DCM dynamics. The proposed algorithm considers double support phases explicitly and is active throughout the motion, i.e., during both single and double support phases. For stumble recovery, we introduce a continuous DCM trajectory adaptation based on the instantaneous tracking error of the swing foot. Our method is highly efficient, computing a push recovery solution within 10 microseconds on the robot hardware. Furthermore, it achieves robust locomotion for large external perturbations, which we demonstrate in simulations and experiments with the humanoid robot TORO.

In the present paper, we propose a novel system-driven adaptive shared control framework in which the autonomous system allocates the authority among the human operator and itself. Authority allocation is based on a metric derived from a Bayesian filter, which is being adapted online according to real measurements. In this way, time-varying measurement noise characteristics are incorporated. We present the stability proof for the proposed shared control architecture with adaptive authority allocation, which includes time delay in the communication channel between the operator and the robot. Furthermore, the proposed method is validated through experiments and a user-study evaluation. The obtained results indicate significant improvements in task execution compared with pure teleoperation.

In the present paper, we first adopt explicit force control from general robotics and embed it into teleoperation systems to enhance the transparency by reducing the effect of the perceived inertia to the human operator and simultaneously improve contact perception. To ensure stability of the proposed teleoperation system considering time-delays, we propose a sequential design procedure based on time domain passivity approach. Experimental results of master-slave teleoperation system, based on KUKA light-weight-robots, for different values of delays are presented. Comparative analysis is conducted considering two existing approaches, namely 2-channel and 4-channel architecture based bilateral controllers, and its results clearly indicate significant improvement in force transparency owing to the proposed method. The proposed system is finally validated considering a real industrial assembly scenario.

Attaching a robotic manipulator to a flying base allows for significant improvements in the reachability and versatility of manipulation tasks. In order to explore such systems while taking advantage of human capabilities in terms of perception and cognition, bilateral teleoperation arises as a reasonable solution. However, since most telemanipulation tasks require visual feedback in addition to the haptic one, real-time (task-dependent) positioning of a video camera, which is usually attached to the flying base, becomes an additional objective to be fulfilled. Since the flying base is part of the kinematic structure of the robot, if proper care is not taken, moving the video camera could undesirably disturb the end-effector motion. For that reason, the necessity of controlling the base position in the null space of the manipulation task arises. In order to provide the operator with meaningful information about the limits of the allowed motions in the null space, this paper presents a novel haptic concept called Null-Space Wall. In addition, a framework to allow stable bilateral teleoperation of both tasks is presented. Numerical simulation data confirm that the proposed framework is able to keep the system passive while allowing the operator to perform time-delayed telemanipulation and command the base to a task-dependent optimal pose.

This paper presents a design of oscillation damping control for the cable-Suspended Aerial Manipulator (SAM). The SAM is modeled as a double pendulum, and it can generate a body wrench as a control action. The main challenge is the fact that there is only one onboard IMU sensor which does not provide full information on the system state. To overcome this difficulty, we design a controller motivated by a simplified SAM model. The proposed controller is very simple yet robust to model uncertainties. Moreover, we propose a gain tuning rule by formulating the proposed controller in the form of output feedback linear quadratic regulation problem. Consequently, it is possible to quickly dampen oscillations with minimal energy consumption. The proposed approach is validated through simulations and experiments.

Lightweight robots are known to be intrinsically elastic in their joints. The established classical approaches to control such systems are mostly based on motor-side coordinates since the joints are comparatively stiff. However, that inevitably introduces errors in the coordinates that actually matter: the ones on the link side. Here we present a new joint-torque controller that uses feedback of the link-side positions. Passivity during interaction with the environment is formally shown as well as asymptotic stability of the desired equilibrium in the regulation case. The performance of the control approach is experimentally validated on DLR's new generation of lightweight robots, namely the SARA robot, which enables this step from motor-side-based to link-sided-based control due to sensors with higher resolution and improved sampling rate.

In this paper, we propose three novel Hardware-in-the-loop simulation (HLS) methods for a fully-actuated orbital robot in the presence of external interactions using On-Ground Facility Manipulators (OGFM). In particular, a fixed-base and a vehicle-driven manipulator are considered in the analyses. The key idea is to describe the orbital robot's dynamics using the Lagrange-Poincaré(LP) equations, which reveal a block-diagonalized inertia. The resulting advantage is that noisy joint acceleration/torque measurements are avoided in the computation of the spacecraft motion due to manipulator interaction even while considering external forces. The proposed methods are a consequence of two facilitating theorems, which are proved herein. These theorems result in two actuation maps between the simulated orbital robot and the physical OGFM. The chief advantage of the proposed methods is physical consistency without level-set assumptions on the momentum map. We validate this through experiments on both types of OGFM in the presence of external forces. Finally, the effectiveness of our approach is validated through a HLS of a fully-actuated orbital robot while interacting with the environment.

The control of a robot in its task space is a standard approach nowadays. If the system is kinematically redundant with respect to this goal, one can even execute additional subtasks simultaneously. By utilizing null space projections, for example, the whole stack of tasks can be implemented within a strict task hierarchy following the order of priority. One of the most common methods to track multiple task-space trajectories at the same time is to feedback-linearize the system and dynamically decouple all involved subtasks, which finally yields the exponential stability of the desired equilibrium. In this article, we provide a hierarchical multi-objective controller for trajectory tracking that ensures both asymptotic stability of the equilibrium and a desired contact impedance at the same time. In contrast to the state of the art in prioritized multi-objective control, feedback of the external forces can be avoided and the natural inertia of the robot is preserved. The controller is evaluated in simulations and on a standard lightweight robot with torque interface. The approach is predestined for precise trajectory tracking where dedicated and robust physical-interaction compliance is crucial at the same time.

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.

Humanoid robots typically display locomotion patterns that include walking with flat foot-ground contact, and knees slightly bent. However, analysis of human gait indicate that several physiological mechanisms like stretched knees, heel-strike and toe push-off increase the step length and energetic efficiency of locomotion. This paper presents an implementation of two of those mechanisms, namely stretched knees and push-off, on a quasi-static whole-body balancing controller. The influence of such mechanisms on the kinematic capabilities of the DLR humanoid robot TORO is analyzed in different experiments, and their benefits are thoroughly discussed. As a result, the energetic savings of balancing with stretched knees are shown to be of reduced magnitude with respect to the overall power consumption of the robot, and the ability of TORO for negotiating stairs is greatly enhanced.

High risk of a collision between rotor blades and the obstacles in a complex environment imposes restrictions on the aerial manipulators. To solve this issue, a novel system cable-Suspended Aerial Manipulator (SAM) is presented in this paper. Instead of attaching a robotic manipulator directly to an aerial carrier, it is mounted on an active platform which is suspended on the carrier by means of a cable. As a result, higher safety can be achieved because the aerial carrier can keep a distance from the obstacles. For self-stabilization, the SAM is equipped with two actuation systems: winches and propulsion units. This paper presents an overview of the SAM including the concept behind, hardware realization, control strategy, and the first experimental results.

This paper tackles a friction compensation problem without using a friction model. The unique feature of the proposed friction observer is that the nominal motor-side signal is fed back into the controller instead of the measured signal. By doing so, asymptotic stability and passivity of the controller are maintained. Another advantage of the proposed observer is that it provides a clear understanding for the stiction compensation which is hard to be captured in model-free approaches. This allows to design observers that do not overcompensate for the stiction. The proposed scheme is validated through simulations and experiments.

Future planetary rovers will gain the ability to manipulate their environment in addition to the maneuverability of current systems. For dedicated contact interaction, Cartesian impedance control is a well-established approach from numerous terrestrial applications. In this paper we will present a whole-body Cartesian impedance controller for a planetary rover equipped with a robotic arm. In contrast to classical terrestrial whole-body controllers, the issue of proper wheel force distribution will be addressed within the control framework. A global optimization solves this redundancy in the over-actuation of the mobile base while additionally handling the kinematic redundancy in the serial kinematic sub-chain of the robot. The approach is experimentally validated on the DLR Lightweight Rover Unit. It can be used for versatile manipulation in rough terrain such as encountered in planetary exploration or terrestrial search-and-rescue scenarios.

This paper presents methods that facilitate the implementation of dynamic walking on torque-controlled robots in real world experiments. The work uses the Divergent Component of Motion (DCM) for walking trajectory generation and control. The DCM controller is embedded into a whole-body controller (WBC) that produces a full-body walking behavior. While in simulation the combination of DCM and WBC is sufficient for achieving sophisticated walking gaits, during our initial experiments several real-world issues, detailed in this paper, prevented the original control framework from functioning. This work presents the improvements to the original control framework that enabled a breakthrough on the way to achieving torque-based dynamic walking on a real robot.

In this paper we address the problem of controlling a robotic system mounted on an actuated floating base for space applications. In particular, we investigate the stability issues due to the low rate of the base control unit. We propose a passivity-based stabilizing controller based on the time domain passivity approach. The controller uses a variable damper regulated by a designed energy observer. The effectiveness of the proposed strategy is validated on a base-manipulator multibody simulation.

Robotic teleoperation is a key technology for a wide variety of fields. Teleoperating a humanoid in particular is essential as it allows the user to act remotely on an interface designed especially for humans, e.g., in a space station, or operating tools and machinery in disaster scenarios. This paper presents a ‘task-relevant’ haptic interface for humanoid teleoperation, which bridges the gap between the task at hand and the balance of the robot. The operator is given command over the humanoid's hands and is informed through haptic cues about the impact of her/his potential actions on the robot’ stability. Moreover, a null-space autonomous controller acts in the operator's null-space to provide her/him with a wider workspace and help in the successful execution of the task. The architecture is designed to top an existing compliance controller for a torque-controlled humanoid robot. Experiments on the humanoid robot TORO are reported to demonstrate the feasibility and effectiveness of the approach.

We present a new approach for Cartesian impedance control of compliantly actuated robots with possibly nonlinear spring characteristics. It reveals a remarkable stiffness and damping range in the experimental evaluation. The most interesting contribution, is the way the desired closed-loop dynamics is designed. Our control concept allows to add a desired stiffness and damping directly on the end-effector, while leaving the system structure intact. The intrinsic inertial and elastic properties of the system are preserved. This is achieved by introducing new motor coordinates that reflect the desired spring and damper terms. Theoretically, by means of additional motor inertia shaping it is possible to make the end-effector interaction behavior with respect to external loads approach, arbitrarily close, the interaction behavior that is achievable by classical Cartesian impedance control on rigid robots. The physically motivated design approach allows for an intuitive understanding of the resulting closed-loop dynamics. We perform a passivity and stability analysis on the basis of al physically motivated storage and Lyapunov function.

This paper presents a passive compliance control for aerial manipulators to achieve stable environmental interactions. The main challenge is the absence of actuation along body-planar directions of the aerial vehicle which might be required during the interaction to preserve passivity. The controller proposed in this paper guarantees passivity of the manipulator through a proper choice of end-effector coordinates, and that of vehicle fuselage is guaranteed by exploiting time domain passivity technique. Simulation studies validate the proposed approach.

This paper proposes an integration of multi-body and actuator control for multi-contact balancing for robots with highly elastic joints. Inspired by the structure preserving control concept for series-elastic fixed-base robots, the presented approach aims to minimize the control effort by keeping the system structure intact. Balancing on multiple contacts requires to solve the force distribution problem. In locomotion, contacts change quickly, requiring a swift redistribution of contact forces. This is a challenge for elastic robots as the actuator dynamics and limits prevent instantaneous changes of contact forces. The proposed dynamically consistent force distribution is implemented as a model predictive controller which resolves redundancy while complying with contact force and actuator constraints.

Despite the substantial progression of autonomous driving systems, their application is often limited e.g. due to safety margins which can be caused by uncertainties in the environment reconstruction. Then, via teleoperation as a fallback solution, a human-in-the-loop can be introduced as the main decision maker. However, high delay in the communication channel distorts the performance of direct force feedback teleoperation for example in space or disaster scenarios. On the other hand, model-mediated teleoperation can provide instantaneous and even predictive force feedback to the user, but the performance is limited due to state mismatches, incomplete models, model errors and the modeling challenges of complex wheel-ground contacts. Therefore, in this paper we introduce the concept of extended model-mediated teleoperation with a car like interface for mobile robots by fusing local fictitious and remote force feedback, which can be measured, computed or fictitious. We provide a method to guarantee stability of the extended model-mediated teleoperation (involving time delay, multilateral coupling, fictitious force feedback and permanent updates of the local model) based on the passivity theorem. The benefits of the approach are highlighted by human-in-the-loop experiments with a wheeled mobile robot.

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 paper 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 elastic structure preserving (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 ESP 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 Hand Arm System from the German Aerospace Center (DLR), a variable stiffness robot arm, 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, multijoint robots with nonlinear elastic elements.

This paper presents that the joint torque control capability can be enhanced by adding physical damper to a series elastic actuator (SEA). Joint torque tracking of standard SEA has known limitations that the torque dynamics has an relative order of two, and, as a consequence, the torque controller often requires acceleration feedback when the desired torque is defined by a function of velocity (for example, compliance control). This limitation can be removed by introducing physical damping, reducing the relative degree of torque dynamics by one. Based on this observation, we design a robust controller using the disturbance observer technique. The resulting control law is given by a feed-forward term combined with PI control. The proposed controller is verified in simulation and experiment.

This paper presents a new method for planning and controlling dynamic multi-contact motions for humanoid robots. Our motion planner takes a sequence of multi-contact stances and generates closed-form reference trajectories for the robot center of mass (CoM) position, velocity, and acceleration, based on the concept of Divergent Component of Motion (DCM). The timing of the contact transitions and the end-effector trajectories are automatically computed such that the motion is feasible with respect to kinematic and dynamic constraints. We verify the constraints using a simplified model of the robot to achieve a very fast planner that finds a feasible solution within a few seconds. The reference trajectories serve as inputs to a passivity-based whole-body controller which includes a DCM controller for tracking the CoM trajectory. We demonstrate the robustness of our approach in simulation and experiments with the humanoid robot TORO.

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.

This paper presents a novel multi-step closed-form walking trajectory generator based on the concept of Divergent Component of Motion (DCM) that guarantees smoothness of all resulting reference trajectories. Further, we introduce an analytical method for footstep adjustment to recover from strong disturbances. The DCM trajectory is adjusted to guarantee smoothness of control outputs. Additionally, we present a momentum-based disturbance observer that improves robustness w.r.t. strong continuous perturbations. The proposed methods are verified in simulations.

Introducing humanoid robots in areas where space is limited, for example in search-and-rescue scenarios or industrial manufacturing, represents a huge challenge, especially when the environment is cluttered and unknown. The robot should be capable of utilizing multiple contact points distributed across the entire body and not just its feet and hands. Extra contacts on the whole body, for instance including the knees and elbows, enable the robot to increase its agility and robustness by enhancing the support polygon. This paper applies our passivity-based approach for hierarchical whole-body control including balancing to scenarios involving contacts distributed all over the body of the robot as required in confined spaces. The approach is experimentally validated on the torque-controlled humanoid robot TORO to demonstrate the general applicability of the presented framework.

In this paper, a tracking control approach for robot assisted landing of UAV rotorcraft, such as multicopters and helicopters, is presented. The aim is to safely land these type of flying vehicles under side wind conditions and on moving surfaces using a robot manipulator arm mounted on the ground. In our previous work, we have considered light UAVs compared to the robot's payload capabilities. In this work, we present a method that enables to realize robot assisted landing for arbitrary combinations of aerial vehicles and robot arms. We show that the combined system is overactuated. This allows to distribute the workload and enables to assist heavy rotorcraft, whose weight would otherwise exceed the nominal payload of the robot arm. The performance of the controller is evaluated in numerical simulations as well as in experiments using a custom-built hexacopter and a KUKA/DLR light-weight robot.

Ensuring safety is a primary goal in physical human-robot interaction. In various collision experiments it was found that the robot's effective mass, velocity, and geometry are the key parameters which influence the human injury severity during an impact. Recently, a velocity controller was proposed that limits the robot speed to a biomechanically safe value, taking into account the mass and the curvature in the direction of movement for a given point of interest. The mass and the geometry depend on the mechanical design, however, the effective mass also depends on the robot configuration. In this paper, we exploit the redundant degree(s) of freedom of a joint torque controlled seven- and eight-DOF robot to minimize the effective mass without affecting the desired Cartesian end-effector trajectory and with the goal to improve the performance of the safe velocity controller at the same time. Given recent results in robotics injury analysis, we analyze when such a redundancy resolution scheme actually improves safety. For the considered robots, we find reflected mass extrema that can be obtained by null space motions, and propose a real-time, torque-based redundancy resolution scheme, which is finally verified in experiments.

Series-elastic and viscoelastic robots can provide performance gains in applications with high dynamics. Harnessing these, requires an understanding of the dynamics of the system, which can be gained using optimization-based methods. The result are motions which make optimal use of the intrinsic behavior, possibly exceeding the performance of an equivalent rigid-body robot. We present a collocation framework which enables both automatic computation of contact-switching patterns and allows the full utilization of the dynamics of the compliant system. The formulation also addresses the problem of redundant torque generation in viscoelastic actuators. The effectiveness of this method was demonstrated in simulations as well as experiments with a compliant bipedal robot. The approach is capable of providing gait primitives, longer gait sequences containing multiple steps as well as generating extremely dynamic motions, e.g. somersaults.

While only continuous motions are possible, the way in which contacts appear and disappear confers to legged locomotion a characteristic discontinuous nature that is traditionally shared by the algorithms used for legged locomotion planning. In this paper, we show that this discontinuous nature can disappear if the notion of collision is well redefined and we efficiently solve two different practical problems of legged locomotion planning with algorithms based on an approach that establishes a bridge between discrete and continuous planning. The first problem consists of reactive footstep planning with a biped robot and the second one consists of nongaited locomotion planning with a hexapod.

Flying in unknown environments may lead to unforeseen collisions, which may cause serious damage to the robot and/or its environment. In this context, fast and robust collision detection combined with safe reaction is, therefore, essential and may be achieved using external wrench information. Also, deliberate physical interaction requires a control loop designed for such a purpose and may require knowledge of the contact wrench. In principle, the external wrench may be measured or estimated. Whereas measurement poses large demands on sensor equipment, additional weight, and overall system robustness, in this paper we present a novel model-based method for external wrench estimation in flying robots. The algorithm is based on the onboard inertial measurement unit and the robot's dynamics model only. We design admittance and impedance controllers that use this estimate for sensitive and robust physical interaction. Furthermore, the performance of several collision detection and reaction schemes is investigated in order to ensure collision safety. The identified collision location and associated normal vector located on the robot's convex hull may then be used for sensorless tactile sensing. Finally, a low-level collision reflex layer is provided for flying robots when obstacle avoidance fails, also under wind influence. Our experimental and simulation results show evidence that the methodologies are easily implemented and effective in practice.

This paper presents a control method to implement trajectory tracking and disturbance rejection characteristics for the link-side dynamics of compliantly actuated robots with nonlinear spring characteristics. This is achieved by introducing new motor coordinates reflecting the damping and feedforward terms and shaping the dynamics of the motor such that it structurally equals the dynamics in the original coordinates. Thus, the approach achieves the control goal while changing the original plant dynamics only to a minimum extent. Passivity, stability, and convergence properties of the closed loop dynamics are proven. The performance of the control approach has been experimentally evaluated on the variable stiffness robot arm DLR Hand Arm System, where the stiffness in each of the joints is highly nonlinear. To our best knowledge, this is the first experimentally validated tracking controller for compliantly actuated robots with nonlinear elastic elements.

Admittance control is a well-established and popular control strategy in modern robotics. However, the standard admittance controller has several limitations. First, the passivity can be guaranteed by finding a set of control parameters that makes the admittance function positive real. However, this approach cannot be applied to multi degrees-of-freedom robot because it requires transfer function analysis. Second, standard admittance controller is not suitable when the system is exposed to unexpected environmental interaction (of which interaction force is not measured) due to the wall sticking effect. To overcome these limitations, this paper proposes an admittance controller of which structure can be constructed by feedback interconnection of passive subsystems. The proposed approach was verified using experiments and simulations.

This paper works toward bridging the gap between observations and analysis of human-running motions, i.e., motion science and robust humanoid robot control. It is based on the concept of biologically inspired deadbeat (BID) control, which facilitates both 3D running on flat ground and on 3D stepping stones. Further contributions include explicit foot step targeting during running, leg crossover avoidance, and the embedding of BID control into a quadratic-program-based whole-body controller. The controller is based on the encoding of leg forces and center-of-mass (CoM) trajectories during stance as polynomial splines, allowing for intuitive and purely analytical controller design. It allows a real-time implementation, is highly robust against perturbations, and enables versatile running patterns. This paper provides a method for purely analytical foot-step targeting, introduces a new method to increase kinematic feasibility on complex robot models, and presents advanced whole-body running simulations, including high-speed running and push recovery. The paper closes the circle to human motion science by comparing BID-based CoM trajectories and ground reaction forces to data from human-running experiments.

This paper presents an online learning framework for improving the robustness of zero-moment point (ZMP)-based biped walking controllers. The key idea is to learn a feedforward compensative ZMP (CZMP) trajectory from measured ZMP errors during repetitive walking motions by applying iterative learning control theory. The learned CZMP trajectory adjusts the reference ZMP and reduces the effect of unmodeled dynamics at the pattern-generation stage. From individual learned CZMP trajectories of typical walking parameters, we can build up a CZMP database. This database can be used for generating an initial CZMP whenever a new walking pattern is executed. A prediction from the database is done by k-nearest neighbor regression based on the Mahalonobis distance. Compared with state-of-the-art model-based methods, the proposed learning approach is model free and allows online adaptation to constant unknown disturbances. Enhanced walking robustness can be observed from reduced average ZMP error and more robust reaction against external disturbances on the DLR humanoid robot TORO.

This paper presents an adaptive and compliant approach-to-grasp strategy for multi-finger robotic hands, to improve the performance of autonomous grasping when encountering object position uncertainties. With the proposed approach-to-grasp strategy, the first robot finger to experience unexpected impact would pause its movement in a compliant manner, and remains in contact with the object to minimize the unplanned motion of the target object. At the same time, the remainder of the fingers continuously, adaptively move toward re-adjusted grasping positions with respect to the first finger in contact with the object, without the need for on-line re-planning or re-grasping. An adaptive grasp control strategy based on spatial virtual spring framework is proposed to achieve local (e.g. not resorting to the robotic arm) in-hand adjustments of the fingers not yet in contact. As such, these fingers can be adaptively driven to the adjusted desired position to accomplish the grasp. Experimental results demonstrate that significantly larger position errors with respect to the hand workspace can be accommodated with the proposed adaptive compliant grasp control strategy. As much as 391% increase in position error area coverage has been achieved. Finally, beyond the quantitative analysis, additional observations during the extensive experiment trials are discussed qualitatively, to help examine several open issues, and further understand the approach-to-grasp phases of the robot hand tasks.

Biped walking control based on simplified models relies much on online feedback stabilizers to compensate the zero-moment point (ZMP) error which partially comes from the model inconsistency of pattern generation. Inspired by the fact that human improves the performance by practicing a task for multiple times, this paper presents an online learning control framework for improving the robustness during the dominant repetitive phases of walking. The key idea is to learn a compensative feedforward ZMP term from previous ZMP error trajectories in order to achieve better ZMP tracking. Based on the iterative learning control theory, the learning process is conducted online continuously with minimal iteration of two footsteps, which can practically run in parallel with state-of-the-art walking controllers. A varying forgetting factor is designed to reduce the influence of the landing impact. Convergence of the learning control algorithm and improved ZMP tracking performance is verified both in dynamics simulation and experiment on the DLR humanoid robot TORO.

This paper introduces a Biologically Inspired Dead-beat (BID) controller for bipedal running in 3D. The controller runs in real-time, is extremely robust against perturbations and allows for versatile running patterns. It is based on the encoding of leg forces and CoM trajectories during stance as polynomial splines, allowing for intuitive and primarily analytical controller design. The performance of the control framework is tested in various simulations for a bipedal point-mass model.

In this paper, the concept of divergent component of motion (DCM, also called “Capture Point”) is extended to 3-D. We introduce the “Enhanced Centroidal Moment Pivot point” (eCMP) and the “Virtual Repellent Point” (VRP), which allow for the encoding of both direction and magnitude of the external forces and the total force (i.e., external plus gravitational forces) acting on the robot. Based on eCMP, VRP, and DCM, we present methods for real-time planning and tracking control of DCM trajectories in 3-D. The basic DCM trajectory generator is extended to produce continuous leg force profiles and to facilitate the use of toe-off motion during double support. The robustness of the proposed control framework is thoroughly examined, and its capabilities are verified both in simulations and experiments.

This paper presents an online methodology for imitating human walking motion of a humanoid robot in task and joint space simultaneously. Two aspects are essential for a successful walking imitation: stable footprints represented in task space and motion similarity represented in joint space. The human footprints are recognized from the captured motion data and imitated by the robot through conventional zero-moment point (ZMP) control scheme. Additionally we focus on similar knee joint trajectories for the motion similarity, which are related to knee stretching and swing leg motion. The inverse kinematics suffers from three problems: knee singularity, strongly conflicting tasks and underactuation. We formulate this problem as a quadratic programming (QP) with dynamic equality and inequality constraints. The discontinuity of dynamic task switching is solved by introducing an activation buffer, resulting in a cascaded QP form. Finally we evaluate the effectiveness of the proposed approach on the DLR humanoid robot TORO.

Robots with joint elasticity find increasing interest in many research areas. A common design goal is to achieve as little mechanical joint damping as possible. To still achieve system damping often control systems are used. Here, we present a model-free approach to achieve damping via exploiting the kinetic to potential energy transformation process of the robot mass and the joint elasticity. The controller acts in an energetically passive way and is applicable to multi-joint systems. The theoretical findings and simulations are substantiated by experiments on the DLR Hand Arm System.

This paper works with the concept of Divergent Component of Motion (DCM), also called `(instantaneous) Capture Point'. We present two real-time DCM trajectory generators for uneven (three-dimensional) ground surfaces, which lead to continuous leg (and corresponding ground reaction) force profiles and facilitate the use of toe-off motion during double support. Thus, the resulting DCM trajectories are well suited for real-world robots and allow for increased step length and step height. The performance of the proposed methods was tested in numerous simulations and experiments on IHMC's Atlas robot and DLR's humanoid robot TORO.

Whole arm manipulation (WAM) allows robotic manipulators to grasp or even manipulate bulky and heavy objects. The idea is that a robot basically wraps around a bulky object to grasp it. This furthermore allows to grasp relative heavy objects, since the center of gravity of the object is located more closely to the first joints of the robot. Whole arm manipulation significantly increases the manipulation skills of a robot and makes it more useful in human environment and was already applied to carry bulky and heavy objects [9], [10], or a human dummy [11]. In the past only few controllers dedicated for WAM were presented. In this paper we propose a new impedance controller on object level that considers the grasp of a bulky object with contacts on the (passive) robot chest and on each forearm of a two-armed robot system. This included to locate the object frame along with the passive contact frame, so that only object rotations need to be commanded. The controller was successfully implemented on DLR Justin. A gymnastic ball with a diameter of 0.45 m was securely grasped and the object was rotated in three dimensions.

This work presents a new approach to whole-body control for balancing and posture stabilization of humanoid robots utilizing an optimization of contact forces in combination with Model Predictive Control. To perform tasks that require multiple contacts, like manipulation or crawling, the controller allows the robot to use a subset of its end effectors to apply a desired wrench to the environment. The remaining end effectors are used for balancing while taking into account the wrenches originating from the manipulation. Due to the prediction the controller is able to react to changes in the control inputs in advance. This approach is evaluated in simulation with the humanoid robot TORO.

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.

Robots with a large number of actuated degrees of freedom are usually redundant w.r.t. a given task. That kinematic redundancy can be utilized to execute additional tasks simultaneously, e. g. via null space projection techniques. We introduce a new representation of hierarchical robot dynamics which are based on a set of particular null space velocities. Dynamic consistency is preserved, and strict compliance with the order of priority is ensured at all times due to a power-conserving cancellation of coupling terms by active control. No external force measurements have to be performed. We show asymptotic stability of the generic closed-loop system with an arbitrary number of hierarchy levels. Several simulations confirm our results.

In this paper, we extend the Divergent Component of Motion (DCM, also called `Capture Point') to 3D. We introduce the “Enhanced Centroidal Moment Pivot point” (eCMP) and the “Virtual Repellent Point” (VRP), which allow for the encoding of both direction and magnitude of the external (e.g. leg) forces and the total force (i.e. external forces plus gravity) acting on the robot. Based on eCMP, VRP and DCM, we present a method for real-time planning and control of DCM trajectories in 3D. We address the problem of underactuation and propose methods to guarantee feasibility of the finally commanded forces. The capabilities of the proposed control framework are verified in simulations.

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.

In this work we present a framework for kinesthetic teaching and iterative refinement of whole body motions. For detection of external forces we apply a momentum based disturbance observer known from manipulator control to the floating-base model of a humanoid robot. These external forces are used as a trigger for implementing a compliant behavior at the interaction point and are integrated into a predictive balancing algorithm. For representation of the motion data, a hidden Markov model is used, which allows for an iterative update of the discrete motion states as well as a smooth generation of continuous motion data. Finally, we present an application of these algorithms on the humanoid robot TORO.

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.

In this paper the generation of walking gaits for biped robots is addressed as a nonlinear optimization problem. The latter presents an efficient formulation, which only requires parameterizing the joint states and does not require to integrate the equations of motion. The results of the optimization are applied to a real robot, with the aid of a suitable stabilizing controller. The final gain in optimized cost is assessed, for the real system. The experimental results confirm the effectiveness of the method.

This video presents our recent research on the integration of physical human-robot interaction (pHRI) into imitation learning. First, a marker control approach for real time human motion imitation is shown. Secondly, physical coaching in addition to observational learning is applied for the incremental learning of motion primitives. Last, we extend imitation learning to learning pHRI which includes the establishment of intended physical contacts. The proposed methods were implemented and tested using the IRT humanoid robot and DLR's humanoid upper-body robot Justin.

This paper builds up on the Capture Point concept and exploits the simple form of the dynamical equations of the Linear Inverted Pendulum model when formulated in terms of the center of mass and the Capture Point. The presented methods include (i) the derivation of a Capture Point (CP) control principle based on the natural dynamics of the linear inverted pendulum (LIP), which stabilizes the walking robot and motivates (ii) the design of a CP tracking and a CP end-of-step controller. The exponential stability of the CP control law is proven. Tilting is avoided by proper projection of the commanded zero moment point. The robustness of the derived control algorithms is analyzed analytically and verified in simulation and experiments.

The Time Domain Passivity Control Approach (TDPA) is a powerful tool to guarantee passive interaction between a robot and its environment. Rather than establishing fixed control parameters to keep the system stable in any possible environment, the TDPA observes the energy flow due to the interaction and applies a dissipative term in the case the interaction becomes active. In a robot manipulator the rationale behind the Passivity Controller requires a criterion on how to distribute the energy to be dissipated among the multiple joints and must be adjusted according to the general control goal of the application. This paper presents a method for distributing the dissipation between decoupled subspaces of a redundant manipulator, prioritizing dissipation in the null-space. The method allows to preserve passivity while avoiding disturbance of the general control goal defined in the task-space. Thus the general control goal can, to some extent, be as well decoupled from passivity considerations and thus a less conservative controller can be achieved. The approach is sustained with a numerical simulation.

Impedance and Admittance Control are two distinct implementations of the same control goal. It is well known that their stability and performance properties are complementary. In this paper, we present a hybrid system approach, which incorporates Impedance and Admittance Control as two extreme cases of one family of controllers. This approach allows to continuously switch and interpolate between Impedance and Admittance Control. We compare the basic stability and performance properties of the resulting controllers by means of an extensive case study of a one-dimensional system and present an experimental evaluation using the KUKA-DLR-lightweight arm.

We present an approach for kinesthetic teaching of motion primitives for a humanoid robot. The proposed teaching method allows for iterative execution and motion refinement using a forgetting factor. During the iterative motion refinement, a confidence value specifies an area of allowed refinement around the nominal trajectory. A novel method for continuous generation of motions from a hidden Markov model (HMM) representation of motion primitives is proposed, which incorporates relative time information for each state. On the real-time control level, the kinesthetic teaching is handled by a customized impedance controller, which combines tracking performance with soft physical interaction and allows to implement soft boundaries for the motion refinement. The proposed methods were implemented and tested using DLR's humanoid upper-body robot Justin.

In this paper, mimetic communication is extended to human-robot interaction tasks, in which physical contact transitions must be handled. The mimetic communication consists of imitation learning for learning low level motion primitives and a higher level interaction learning stage in which also the information about the human-robot contacts is included. For the imitation learning, Cartesian marker data from a motion capture system is used. A modification of the low level marker trajectory following algorithm is presented, which allows to reshape the trajectory of the motion primitive in accordance with the human hand motion in real-time. Moreover, for performing safe contact motion, an appropriate impedance controller is integrated into the setting. All the presented concepts are evaluated in experiments with a humanoid robot.

In this paper, a position based impedance controller (i.e. admittance controller) is designed by utilizing measurements of a force/torque sensor, which is mounted at the robot's base. In contrast to conventional force/torque sensing at the end-effector, placing the sensor at the base allows to implement a compliant behavior of the robot not only with respect to forces acting on the end-effector but also with respect to forces acting on the robot's structure. The resulting control problem is first analyzed in detail for the simplified one-degree-of-freedom case in terms of stability and passivity. Then, an extension to the Cartesian admittance control of a robot manipulator is discussed. Furthermore, it is shown how the steady state properties of the underlying position controller can be taken into account in the design of the outer admittance controller. Finally, a simulation study of the Cartesian admittance controller applied to a three-degrees-of-freedom manipulator is presented.

In this paper a compliance control law for kinematically redundant manipulators is proposed. The controller contains a Cartesian compliance part and a nullspace compliance part which are complemented by a power-conserving decoupling term. The approach deliberately avoids inertia shaping in order to obtain a control law which does not require the measurement of external forces and becomes less sensitive with respect to model uncertainties. While the controller formulation explicitly uses nullspace velocity coordinates, no integration of these velocities is required. Except for the kinematic singularities of the manipulator’s Jacobian matrix, no further algorithmic singularities are introduced. Asymptotic stability of the closed-loop system is shown by utilizing semi-definite Lyapunov functions. Finally, a short planar simulation study is presented which validates the effectiveness of the approach.

By controlling complex robotic systems one often has to cope with the situation that different sub-systems are interfaced and controlled by different computers. In this paper the problem of coordinated control of such a system with distributed control structure is addressed. In particular one must handle the transmission delays in the communication between the different computers, which can be considered small but not negligible, since also small delays in the transmission of power variables violate the passivity and therefore may lead to instability. In this paper the wave variables concept is applied to handle the delays and is used in combination with a virtual inertia for designing a Cartesian compliance controller. Therefore, in particular the steady state properties of the wave variable based communication is of interest and leads for the case of small delays to the analogy with a flexible joint robot. In a second step the virtual inertia is eliminated in order to approximate the desired closed loop behavior better. Finally, some simple planar simulations are presented which validate the proposed approach.

The object level control of a dexterous robot hand provides an intuitive high-level interface to solve fine manipulation tasks. In the past, many algorithms were proposed based on a weighted pseudoinverse of the grasp map. In a different approach Stramigioli introduces a virtual object - called "intrinsically passive controller (IPC)". This controller distributes the generalized object forces using coupling springs whose weighting have an intuitive physical meaning. Even though this controller has been known for several years we will present the first experimental results for a four-fingered hand. Furthermore, the term virtual grasp map is introduced and a method to parameterize the stiffness parameters in order to obtain an effective object level stiffness and a damping design is proposed. An implementation of the IPC is tested on the DLR Hand II and its performance is analyzed by manipulating soft and stiff objects.

The current discussion on physical human robot interaction and the related safety aspects, but also the interest of neuro-scientists to validate their hypotheses on human motor skills with bio-mimetic robots, led to a recent revival of tendon-driven robots. In this paper, the modeling of tendon-driven elastic systems with nonlinear couplings is recapitulated. A control law is developed that takes the desired joint position and stiffness as input. Therefore, desired motor positions are determined that are commanded to an impedance controller. We give a physical interpretation of the controller. More importantly, a static decoupling of the joint motion and the stiffness variation is given. The combination of active (controller) and passive (mechanical) stiffness is investigated. The controller stiffness is designed according to the desired overall stiffness. A damping design of the impedance controller is included in these considerations. The controller performance is evaluated in simulation.

In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.

This video presents a humanoid two-arm system developed as a research platform for studying dexterous two-handed manipulation. The system is based on the modular DLR-Lightweight-Robot-III and the DLR-Hand-II. Two arms and hands are combined with a three degrees-of-freedom movable torso and a visual system to form a complete humanoid upper body. The diversity of the system is demonstrated by showing the mechanical design, several control concepts, the application of rapid prototyping and hardware-in-the-loop (HIL) development as well as two-handed manipulation experiments and the integration of path planning capabilities.

The control of humanoid manipulators is very challenging due to the large number of degrees of freedom and the resulting redundancy. Using joint-level control complex planning algorithms are needed to accomplish tasks. For intuitive operation and hence short development times of applications high-level control interfaces are needed. Furthermore, for many tasks it is desirable to define an impedance behavior in task space. In this paper a flexible control law is proposed which offers object-level impedances for two-handed manipulation. The controller structure is based on the well-known compliance control law. The main contributions of this work are the way how to combine several potential functions for two-handed manipulation and the experimental validation of hand-arm coordination. The controller is implemented on DLR's humanoid manipulator Justin and its performance is demonstrated experimentally by unscrewing a can and motion of a grasped box.

This paper presents a novel system for accurate placement of pedicle screws. The system consists of a new light-weight (<10 kg), kinematically redundant, and fully torque controlled robot. Additionally, the pose of the robot tool-center point is tracked by an optical navigation system, serving as an external reference source. Therefore, it is possible to measure and to compensate deviations between the intraoperative and the preoperatively planned pose. The robotic arm itself is impedance controlled. This allows for a new intuitive man-machine-interface as the joint units are equipped with torque sensors: the robot can be moved just by pulling/pushing its structure. The surgeon has full control of the robot at every step of the intervention. The hand-eye-coordination problems known from manual pedicle screw placement can be omitted

In this paper the Cartesian compliance control of a manipulator mounted on a flexible base is considered. The proposed control law aims at achieving a desired stiffness and damping in Cartesian coordinates while taking account of the base flexibility. The controller does not use any measurement of the base motion, however a model of the base stiffness is required. For the closed loop system, asymptotic stability in case of free motion is proven. Furthermore, considering interaction tasks, it is shown that the controlled manipulator system has a useful passivity property

Holding an object and manipulating it in 6D is a key application for multifingered robot hands. In the past many algorithms were proposed based on a weighted pseudoinverse of the grasp map combined with an internal force control. The majority of these algorithms require robust contact detection/tracking and switching controllers. Employing the virtual object introduced by Stramigioli we present an object-level control law. We define a novel virtual object frame based on the robot hand configuration. Our control law takes a desired object frame and desired grasping forces as input, it is passive, has an intuitive physical meaning, and stability is even given in case a finger looses contact with the object. A damping design as a function of the desired object stiffness and the combined hand-object inertia is presented. The performance of the controller is proven in two experiments implemented on the DLR Hand II

The paper presents an impedance controller for a class of underactuated Euler-Lagrange systems based on energy shaping. For shaping the potential energy, feedback variables are introduced, which are functions of the collocated state variables only, but which are statically equivalent to the noncollocated state variables. In this way the passivity of the system can be ensured, while exactly satisfying all steady state requirements formulated in terms of the noncollocated states (such as desired stiffness and desired equilibrium configuration). The method is constructive, allowing the direct formulation of the controller and of the corresponding energy function. The controller additionally uses the noncollocated feedback to shape the kinetic energy. Under some conditions on the potential energy of the plant, the closed loop system can then be seen as a feedback interconnection of passive systems and is proven to be asymptotically stable. Experimental results for a flexible joint robot validate the proposed controller.

The paper presents a Cartesian impedance controller for flexible joint robots based on the feedback of the complete state of the system, namely the motor position, the joint torque and their derivatives. The approach is applied to a quite general robot model, in which also a damping element is considered in parallel to the joint stiffness. Since passivity and asymptotic stability of the controller hold also for varying damping matrices, some possibilities of designing those gain matrices (depending on the actual inertia matrix) are addressed. The passivity of the controller relies on the usage of only motor side measurements for the position feedback. A method is introduced, which provides the exact desired link side stiffness based on this motor position information. Experimental results are validating the proposed controller.

In this paper a novel approach to the Cartesian impedance control problem for robots with flexible joints is presented. The proposed controller structure is based on simple physical considerations, which are motivating the extension of classical position feedback by an additional feedback of the joint torques. The torque feedback action can be interpreted as a scaling of the apparent motor inertia. Furthermore the problem of gravity compensation is addressed. Finally, it is shown that the closed loop system can be seen as a feedback interconnection of passive systems. Based on this passivity property a proof of asymptotic stability is presented.

This paper addresses the problem of impedance control for flexible joint robots based on a singular perturbation approach. Some aspects of the impedance controller, which turned out to be of high practical relevance during applications are then addressed, such as the implementation of nullspace stiffness for redundant manipulators, the avoiding of mass matrix decoupling and the related design of the desired damping matrix. Finally, the proposed methods are validated through measurements on the DLR robot.

This paper addresses the impedance control problem for flexible joint manipulators. An impedance controller structure is proposed, which is based on an exact decoupling of the torque dynamics from the link dynamics. A formal stability analysis of the proposed controller is presented for the general tracking case. Preliminary experimental results are given for a single flexible joint.

This paper addresses the adaptive tracking control of flexible joint manipulators based on the singular perturbation approach. Comparisons between adaptive and nonadaptive tracking controllers are given. Experimental results with the DLR's light weight robot are given for the 2-DOF case.

In the growing field of service robotics the interaction between humans and robots is an important topic. In this paper the interactive features of the kinematically redundant DLR lightweight robot axe presented. At the example of an inverted pendulum the "interactive nullspace motion" is introduced, where the user is able to modify the configuration as a subtask while balancing the pendulum as primary task. Different ways of nullspace interaction are shown, either contact-free by a teach-device or a position tracker, or by touching the robot, whereas the joint torque sensors measure the external touch.