Blended Linear Models for Reduced Compliant Mechanical Systems

We present a method for the simulation of compliant, articulated structures using a plausible approximate model that focuses on modeling endpoint interaction. We approximate the structure's behavior about a reference configuration, resulting in a first order reduced compliant system, or FORK (-1) S. Several levels of approximation are available depending on which parts and surfaces we would like to have interactive contact forces, allowing various levels of detail to be selected. Our approach is fast and computation of the full structure's state may be parallelized. Furthermore, we present a method for reducing error by combining multiple FORK (-1)S models at different linearization points, through twist blending and matrix interpolation. Our approach is suitable for stiff, articulate grippers, such as those used in robotic simulation, or physics-based characters under static proportional derivative control. We demonstrate that simulations with our method can deal with kinematic chains and loops with non-uniform stiffness across joints, and that it produces plausible effects due to stiffness, damping, and inertia.

Coordination of muscle torques stabilizes upright standing posture: an UCM analysis

The control of upright stance is commonly explained on the basis of the single inverted pendulum model (ankle strategy) or the double inverted pendulum model (combination of ankle and hip strategy). Kinematic analysis using the uncontrolled manifold (UCM) approach suggests, however, that stability in upright standing results from coordinated movement of multiple joints. This is based on evidence that postural sway induces more variance in joint configurations that leave the body position in space invariant than in joint configurations that move the body in space. But does this UCM structure of kinematic variance truly reflect coordination at the level of the neural control strategy or could it result from passive biomechanical factors? To address this question, we applied the UCM approach at the level of muscle torques rather than joint angles. Participants stood on the floor or on a narrow base of support. We estimated torques at the ankle, knee, and hip joints using a model of the body dynamics. We then partitioned the joint torques into contributions from net, motion-dependent, gravitational, and generalized muscle torques. A UCM analysis of the structure of variance of the muscle torque revealed that postural sway induced substantially more variance in directions in muscle torque space that leave the Center of Mass (COM) force invariant than in directions that affect the force acting on the COM. This difference decreased when we decorrelated the muscle torque data by randomizing across time. Our findings show that the UCM structure of variance exists at the level of muscle torques and is thus not merely a by-product of biomechanical coupling. Because muscle torques reflect neural control signals more directly than joint angles do, our results suggest that the control strategy for upright stance involves the task-specific coordination of multiple degrees of freedom.

Forward dynamics simulation of human figures on assistive devices using geometric skin deformation model

We present a forward dynamics (FD) simulation technique for human figures when they are supported by assistive devices. By incorporating a geometric skin deformation model, called linear blend skinning (skinning), into rigid-body skeleton dynamics, we can model a time-varying geometry of body surface plausibly and efficiently. Based on the skinning model, we also derive a Jacobian (a linear mapping) that maps contact forces exerted on the skin to joint torques, which is the main technical contribution of this paper. This algorithm allows us to efficiently simulate dynamics of human body that interacts with assistive devices. Experimental results showed that the proposed approach can generate plausible motions and can estimate pressure distribution that is roughly comparable to the tactile sensor data.

Kinodynamically Consistent Motion Retargeting for Humanoids

Human-to-humanoid motion retargeting is an important tool to generate human-like humanoid motions. This retargeting problem is often formulated as a Cartesian control problem for the humanoid from a set of task points in the captured human data. Classically, Cartesian control has been developed for redundant systems. While redundancy fundamentally adds new sub-task capabilities, the degree to which secondary objectives can be faithfully executed cannot be determined in advance. In fact, a robot that exhibits redundancy with respect to an operational task may have insufficient degrees of freedom (DOFs) to satisfy more critical constraints. In this paper, we present a Cartesian space resolved acceleration control framework to handle execution of operational tasks and constraints for redundant and nonredundant task specifications. The approach is well suited for online control of humanoid robots from captured human motion data expressed by Cartesian variables. The current formulation enforces kinematic constraints such as joint limits, self-collisions, and foot constraints and incorporates a dynamically-consistent redundancy resolution approach to minimize costly joint motions. The efficacy of the proposed algorithm is demonstrated by simulated and real-time experiments of human motion replication on a Honda humanoid robot model. The algorithm closely tracks all input motions while smoothly and automatically transitioning between regimes where different constraints are binding.

A model-based approach to predict muscle synergies using optimization: application to feedback control

This paper presents a new model-based method to define muscle synergies. Unlike the conventional factorization approach, which extracts synergies from electromyographic data, the proposed method employs a biomechanical model and formally defines the synergies as the solution of an optimal control problem. As a result, the number of required synergies is directly related to the dimensions of the operational space. The estimated synergies are posture-dependent, which correlate well with the results of standard factorization methods. Two examples are used to showcase this method: a two-dimensional forearm model, and a three-dimensional driver arm model. It has been shown here that the synergies need to be task-specific (i.e., they are defined for the specific operational spaces: the elbow angle and the steering wheel angle in the two systems). This functional definition of synergies results in a low-dimensional control space, in which every force in the operational space is accurately created by a unique combination of synergies. As such, there is no need for extra criteria (e.g., minimizing effort) in the process of motion control. This approach is motivated by the need for fast and bio-plausible feedback control of musculoskeletal systems, and can have important implications in engineering, motor control, and biomechanics.

Hybrid motion/force control of multi-backbone continuum robots

The recent growth of surgical applications exploiting continuum robots demands for new control paradigms that ensure safety by controlling interaction forces of tele-operated end-effectors. In this paper, we present the modeling, sensing and control of multi-backbone continuum robots in a unified framework for hybrid motion/force control. Multi-backbone continuum robots allow to estimate forces and torques at the operational point by monitoring loads along their actuation lines without the need for a dedicated transducer at the operational point. This capability is indeed crucial in emerging fields such as robotic surgery where cost and strict sterilization guidelines prevent the adoption of a dedicated sensor to provide force feedback from the sterile field. To advance further the force sensing capabilities of multi-backbone continuum robots, we present a new framework for hybrid motion and force control of continuum robots with intrinsic force sensing capabilities. The framework is based on a kinetostatic modeling of the multi-backbone continuum robot with, a simplified model for online estimate of the manipulator’s compliance, and a new strategy for merging force and motion control laws in the configuration space of the manipulator. Experimental results show the ability to sense and regulate forces at the operational point and evaluate the framework for shape exploration and stiffness imaging in flexible environments.

Towards versatile legged robots through active impedance control

Robots with legs and arms have the potential to support humans in dangerous, dull or dirty tasks. A major motivation behind research on such robots is their potential versatility. However, these robots come at a high price in mechanical and control complexity. Hence, until they can demonstrate a clear advantage over their simpler counterparts, robots with arms and legs will not fulfill their true potential. In this paper, we discuss the opportunities for versatile robots that arise by actively controlling the mechanical impedance of joints and particularly legs. In contrast to passive elements such as springs, active impedance is achieved by torque-controlled joints allowing real-time adjustment of stiffness and damping. Adjustable stiffness and damping in real-time is a fundamental building block towards versatility. Experiments with our 80 kg hydraulic quadruped robot HyQ demonstrate that active impedance alone (i.e. no springs in the structure) can successfully emulate passively compliant elements during highly dynamic locomotion tasks (running, jumping and hopping); and that no springs are needed to protect the actuation system. Here we present results of a flying trot, also referred to as a running trot. To the best of the authors’ knowledge this is the first time a flying trot has been successfully implemented on a robot without passive elements such as springs. A critical discussion on the pros and cons of active impedance concludes the paper. This article is an extension of our previous work presented at the International Symposium on Robotics Research (ISRR) 2013.

An overview of null space projections for redundant, torque-controlled robots

One step on the way to approach human performance in robotics is to provide joint torque sensing and control for better interaction capabilities with the environment, and a large number of actuated degrees of freedom (DOFs) for improved versatility. However, the increasing complexity also raises the question of how to resolve the kinematic redundancy which is a direct consequence of the large number of DOFs. Here we give an overview of the most practical and frequently used torque control solutions based on null space projections. Two fundamental structures of task hierarchies are reviewed and compared, namely the successive and the augmented method. Then the projector itself is investigated in terms of its consistency. We analyze static, dynamic, and the new concept of stiffness consistency. In the latter case, stiffness information is used in the pseudoinversion instead of the inertia matrix. In terms of dynamic consistency, we generalize the weighting matrix from the classical operational space approach and show that an infinite number of weighting matrices exist to obtain dynamic consistency. In this context we also analyze another dynamically consistent null space projector with slightly different structure and properties. The redundancy resolutions are finally compared in several simulations and experiments. A thorough discussion of the theoretical and empirical results completes this survey.

Robotic hand posture and compliant grasping control using operational space and integral sliding mode control

This paper establishes a novel approach of robotic hand posture and grasping control. For this purpose, the control uses the operational space approach. This permits the consideration of the shape of the object to be grasped. Thus, the control is split into a task control and a particular optimizing posture control. The task controller employs Cylindrical and Spherical coordinate systems due to their simplicity and geometric suitability. This is achieved by using an integral sliding mode controller (ISMC) as task controller. The ISMC allows us to introduce a model reference approach where a virtual mass-spring-damper system can be used to design a compliant trajectory tracking controller. The optimizing posture controller together with the task controller creates a simple approach to obtain pre-grasping/object approach hand postures. The experimental results show that target trajectories can be easily followed by the task control despite the presence of friction and stiction. When the object is grasped, the compliant control will automatically adjust to a specific compliance level due to an augmented compliance parameter adjustment algorithm. Once a specific compliance model has been achieved, the fixed compliance controller can be tested for a specific object grasp scenario. The experimental results prove that the Bristol Elumotion robot hand (BERUL) can automatically and successfully attain different compliance levels for a particular object via the ISMC.

Compliance Control and Human–Robot Interaction: Part II — Experimental Examples

Compliance control is highly relevant to human safety in human–robot interaction (HRI). This paper presents multi-dimensional compliance control of a humanoid robot arm. A dynamic model-free adaptive controller with an anti-windup compensator is implemented on four degrees of freedom (DOF) of a humanoid robot arm. The paper is aimed to compliment the associated review paper on compliance control. This is a model reference adaptive compliance scheme which employs end-effector forces (measured via joint torque sensors) as a feedback. The robot's body-own torques are separated from external torques via a simple but effective algorithm. In addition, an experiment of physical human robot interaction is conducted employing the above mentioned adaptive compliance control along with a speech interface. The experiment is focused on passing an object (a cup) between a human and a robot. Compliance is providing an immediate layer of safety for this HRI scenario by avoiding pushing, pulling or clamping and minimizing the effect of collisions with the environment.

Compliance Control and Human–Robot Interaction: Part 1 — Survey

Compliance control is highly relevant to human safety in human–robot interaction (HRI). This paper presents a review of various compliance control techniques. The paper is aimed to provide a good background knowledge for new researchers and highlight the current hot issues in compliance control research. Active compliance, passive compliance, adaptive and reinforcement learning-based compliance control techniques are discussed. This paper provides a comprehensive literature survey of compliance control keeping in view physical human robot interaction (pHRI) e.g., passing an object, such as a cup, between a human and a robot. Compliance control may eventually provide an immediate and effective layer of safety by avoiding pushing, pulling or clamping in pHRI. Emerging areas such as soft robotics, which exploit the deformability of biomaterial as well as hybrid approaches which combine active and passive compliance are also highlighted.

Toward Reactive Vision-Guided Walking on Rough Terrain: An Inverse-Dynamics Based Approach

This work presents a method to handle walking on rough terrain using inverse dynamics control and information from a stereo vision system. The ideal trajectories for the center of mass (CoM) and the next position of the feet are given by a pattern generator. The pattern generator is able to automatically find the footsteps for a given direction. Then, an inverse dynamics control scheme relying on a quadratic programming optimization solver is used to let each foot go from its initial to final position, controlling also the CoM and the waist. A 3D model reconstruction of the ground is obtained through the robot cameras located on its head as a stereo vision pair. The model allows the system to know the ground structure where the swinging foot is going to step on. Thus, contact points can be handled to adapt the foot position to the ground conditions.

Absolutely stable model-based 2-port force controller for telerobotic applications

Large industrial-like slave robots pose a challenging problem for telerobotic control designers focused on achieving good transparency. The human operator typically feels both the large friction forces and heavy inertial forces inherent to these robots. Force control can be used to attempt and hide these internal forces from the user, but force control is a challenging design problem, especially in situations like telerobotics where it is not clear what the environmental impedance will be at any given moment.

This paper introduces a model-based force controller designed to reject the friction in slave robots to improve the overall transparency of the telerobotic system. The primary objective of the force controller is to ensure the closed loop slave 2-port is absolutely stable such that the controller maintains the robustness of the overall telerobot. An analysis is provided that shows that, in order to achieve absolute stability, a local slave-side force controller cannot hide any of the robot’s inertial forces. It is from this result that model-based force control gets its name as it uses a model of the robot’s inertial properties to reject friction forces without attempting to reject inertial forces.

Quadrupedal locomotion using hierarchical operational space control

This paper presents the application of operational space control based on hierarchical task optimization for quadrupedal locomotion. We show how the behavior of a complex robotic machine can be described by a simple set of least squares problems with different priorities for motion, torque, and force optimization. Using projected dynamics of floating base systems with multiple contact points, the optimization dimensionality can be reduced or decoupled such that the formulation is purely based on the inversion of kinematic system properties. The present controller is extensively tested in various experiments using the fully torque controllable quadrupedal robot StarlETH. The load distribution is optimized for static walking gaits to improve contact stability and/or actuator efficiency under various terrain conditions. This is augmented with simultaneous joint position and torque limitations as well as with an interpolation method to ensure smooth contact transitions. The same control structure is further used to stabilize dynamic trotting gaits under significant external disturbances such as uneven ground or pushes. To the best of our knowledge, this work is the first documentation of static and dynamic locomotion with pure task-space inverse dynamics (no joint position feedback) control.

Task-dependent impedance and implications for upper-limb prosthesis control

Modern-day prosthetic limbs are currently unable to imitate the versatile interaction behaviors of real human arms. Although humans can vary the impedance of their arms, commercially available prosthetic limbs have impedance properties that cannot be directly controlled by users. We investigate the hypothesis that user-selectable prosthesis impedance properties could improve the user’s ability to interact effectively with a variety of environments. We report the results of a series of human subject studies exploring this hypothesis using either a virtual prosthesis or a robot arm as a prosthesis proxy. We observed human performance with different stiffness and damping levels in the prosthesis proxy in two one-degree-of-freedom tasks: (1) a force minimization task and (2) a trajectory tracking task. The virtual prosthesis studies focus on human performance in an ideal simulated system to avoid limitations of a physical implementation, whereas the robot arm study focuses on performance changes that result from limitations of physical robotic hardware. The virtual prosthesis results showed that task-dependent impedance can improve user performance and that users can evaluate the effects of changing impedance. The robot arm results showed similar performance benefits of task-dependent impedance in a physical robotic system. These studies identified areas in which non-ideal characteristics of the physical system limited users’ performance; most notably, the physical system could not achieve the low damping levels that helped subjects reduce contact forces in the virtual prosthesis studies. Thus, we identify some design considerations for prostheses with user-selectable impedance that can achieve useful impedance ranges for improving user performance.

Torque response to external perturbation during unconstrained goal-directed arm movements

It is unclear to what extent control strategies of 2D reaching movements of the upper limbs also apply to movements with the full seven degrees of freedom (DoFs) including rotation of the forearm. An increase in DoFs may result in increased movement complexity and instability. This study investigates the trajectories of unconstrained reaching movements and their stability against perturbations of the upper arm. Reaching movements were measured using an ultrasound marker system, and the method of inverse dynamics was applied to compute the time courses of joint torques. In full DoF reaching movements, the velocity of some joint angles showed multiple peaks, while the bell-shaped profile of the tangential hand velocity was preserved. This result supports previous evidence that tangential hand velocity is an essential part of the movement plan. Further, torque responses elicited by external perturbation started shortly after perturbation, almost simultaneously with the perturbation-induced displacement of the arm, and were mainly observed in the same joint angles as the perturbation torques, with similar shapes but opposite signs. These results indicate that these torque responses were compensatory and contributed to system stabilization.

Humans robustly adhere to dynamic walking principles by harnessing motor abundance to control forces

Human walking dynamics are typically framed in the context of mechanics and energetics rather than in the context of neuromuscular control. Dynamic walking principles describe one helpful theoretical approach to characterize efficient human walking mechanics over many steps. These principles do not, however, address how such walking is controlled step-by-step despite small perturbations from natural variability. Our purpose was to identify neuromechanical control strategies used to achieve consistent and robust locomotion despite natural step-to-step force variability. We used the uncontrolled manifold concept to test whether human walkers select combinations of leading and trailing leg-forces that generate equivalent net-force trajectories during step-to-step transitions. Subjects selected leading and trailing leg-force combinations that generated consistent vertical net-force during step-to-step transitions. We conclude that vertical net-force is an implicit neuromechanical goal of human walking whose trajectory is stabilized for consistent step-to-step transitions, which agrees with the principles of dynamic walking. In contrast, inter-leg-force combinations modulated anterior-posterior net-force trajectories with each step to maintain constant walking speed, indicating that a consistent anterior-posterior net-force trajectory is not an implicit goal of walking. For a more complete picture of hierarchical locomotor control, we also tested whether each individual leg-force trajectory was stabilized through the selection of leg-force equivalent joint-torque combinations. The observed consistent vertical net-force trajectory was achieved primarily through the selection of joint-torque combinations that modulated trailing leg-force during step-to-step transitions. We conclude that humans achieve robust walking by harnessing inherent motor abundance of the joints and legs to maintain consistent step-by-step walking performance.

A FURTHER GENERALIZATION OF TASK-ORIENTED CONTROL THROUGH TASKS PRIORITIZATION

Starting from the operational space and task prioritization framework, presented in [L. Sentis and O. Khatib, Task-oriented control of humanoid robots through prioritization, in Proc. IEEE-Robotics and Autonomous Systems/RSJ International Conf. Humanoid Robots, Santa Monica, CA, USA, November 2004.], this paper proposes an extension and improvement of this approach, to make it applicable to nonholonomic tasks and systems. For the tasks where inequality type conditions have to be fulfilled, such solutions are obtained to ensure as small as possible movements at the joints, while keeping the actuators' driving torques between saturation limits. Having in mind that a prerequisite for realization of any task by biped robot is the maintenance of its upright position, this issue is also in the focus of our study. Instead of keeping the zero-moment point (ZMP) at an exact position, dynamic balance was ensured by allowing the ZMP to be anywhere within the support area. Since the condition for ZMP position is relaxed a smaller number of joints are engaged in the task realization, which enables more tasks to be handled simultaneously. Simulations were performed, and the results proved the validity of the proposed approach. When disturbance was applied compensation behavior emerged.

Identifiability and identification of inertial parameters using the underactuated base-link dynamics for legged multibody systems

In this paper we study the dynamics of multibody systems with the base not permanently fixed to the inertial frame, or more specifically legged systems such as humanoid robots and humans. The issue is to be approached in terms of the identification theory developed in the field of robotics. The under-actuated base-link which characterizes the dynamics of legged systems is the focus of this work. The useful mechanical feature to analyze the dynamics of legged system is proven: the set of inertial parameters appearing in the equation of motion of the under-actuated base is equivalent to the set in the equations of the whole body. In particular, when no external force acts on the system, all of the parameters in the set except the total mass are generally identifiable only from the observation of the free-flying motion. We also propose a method to identify the inertial parameters based on the dynamics of the under-actuated base. The method does not require the measurement of the joint torques. Neither the joint frictions nor the actuator dynamics need to be considered. Even when the system has no external reaction force, the method is still applicable. The method has been tested on both a humanoid robot and a human, and the experimental results are shown.

Effects of a foot placement constraint on use of motor equivalence during human hopping

Humans can robustly locomote over complex terrains even while simultaneously attending to other tasks such as accurate foot placement on the ground. We investigated whether subjects would exploit motor redundancy across the joints of the leg to stabilize overall limb kinematics when presented with a hopping task that constrained foot placement position. Subjects hopped in place on one leg (2.2 Hz) while having to place their foot into one of three target sizes upon landing (0.250, 0.063, 0.010 m(2)). As takeoff and landing angles are critical to this task performance, we hypothesized smaller target sizes would increase the need to stabilize (i.e., make more consistent) the leg orientation through motor equivalent combinations of segment angles. As it was not critical to the targeting task, we hypothesized no changes for leg length stabilization across target size. With smaller target sizes, we saw total segment angle variance increase due to greater signal-dependent noise associated with an increased activation of leg extensor muscles (medial and lateral gastrocnemius, vastus medialis, vastus lateralis and rectus femoris). At smaller target sizes, more segment angle variance was aligned to kinematic deviations with the goal of maintaining leg orientation trajectory. We also observed a decrease in the variance structure for stabilizing leg length at the smallest target conditions. This trade-off effect is explained by the nearly orthogonal relationship between the two goal-equivalent manifolds for leg length vs. leg orientation stabilization. Our results suggest humans increasingly rely on kinematic redundancy in their legs to achieve robust, consistent locomotion when faced with novel conditions that constrain performance requirements. These principles may generalize to other human locomotor gaits and provide important insights into the control of the legs during human walking and running.