David J. Braun

Robots Driven by Compliant Actuators: Optimal Control Under Actuation Constraints

Anthropomorphic robots that aim to approach human performance agility and efficiency are typically highly redundant not only in their kinematics but also in actuation. Variable-impedance actuators, used to drive many of these devices, are capable of modulating torque and impedance (stiffness and/or damping) simultaneously, continuously, and independently. These actuators are, however, nonlinear and assert numerous constraints, e.g., range, rate, and effort limits on the dynamics. Finding a control strategy that makes use of the intrinsic dynamics and capacity of compliant actuators for such redundant, nonlinear, and constrained systems is nontrivial. In this study, we propose a framework for optimization of torque and impedance profiles in order to maximize task performance, which is tuned to the complex hardware and incorporating real-world actuation constraints. Simulation study and hardware experiments 1) demonstrate the effects of actuation constraints during impedance control, 2) show applicability of the present framework to simultaneous torque and temporal stiffness optimization under constraints that are imposed by real-world actuators, and 3) validate the benefits of the proposed approach under experimental conditions.

A Control Approach for Actuated Dynamic Walking in Biped Robots

This paper presents an approach for the closed-loop control of a fully actuated biped robot that leverages its natural dynamics when walking. Rather than prescribing kinematic trajectories, the approach proposes a set of state-dependent torques, each of which can be constructed from a combination of low-gain spring-damper couples. Accordingly, the limb motion is determined by interaction of the passive control elements and the natural dynamics of the biped, rather than being dictated by a reference trajectory. In order to implement the proposed approach, the authors develop a model-based transformation from the control torques that are defined in a mixed reference frame to the actuator joint torques. The proposed approach is implemented in simulation on an anthropomorphic biped. The simulated biped is shown to converge to a stable, natural-looking walk from a variety of initial configurations. Based on these simulations, the mechanical cost of transport is computed and shown to be significantly lower than that of trajectory-tracking approaches to biped control, thus validating the ability of the proposed idea to provide efficient dynamic walking. Simulations further demonstrate walking at varying speeds and on varying ground slopes. Finally, controller robustness is demonstrated with respect to forward and backward push-type disturbances and with respect to uncertainty in model parameters.

Optimal variable stiffness control: formulation and application to explosive movement tasks

It is widely recognised that compliant actuation is advantageous to robot control once dynamic tasks are considered. However, the benefit of intrinsic compliance comes with high control complexity. Specifically, coordinating the motion of a system through a compliant actuator and finding a task-specific impedance profile that leads to better performance is known to be non-trivial. Here, we propose an optimal control formulation to compute the motor position commands, and the associated time-varying torque and stiffness profiles. To demonstrate the utility of the approach, we consider an “explosive” ball-throwing task where exploitation of the intrinsic dynamics of the compliantly actuated system leads to improved task performance (i.e., distance thrown). In this example we show that: (i) the proposed control methodology is able to tailor impedance strategies to specific task objectives and system dynamics, (ii) the ability to vary stiffness can be exploited to achieve better performance, (iii) in systems with variable physical compliance, the present formulation enables exploitation of the energy storage capabilities of the actuators to improve task performance. We illustrate these in numerical simulations, and in hardware experiments on a two-link variable stiffness robot.

Exploiting variable stiffness in explosive movement tasks

It is widely recognised that compliant actuation is advantageous to robot control once high-performance, explosive tasks, such as throwing, hitting or jumping are considered. However, the benefit of intrinsic compliance comes with high control complexity. Specifically, coordinating the motion of the system through a compliant actuator and finding a task-specific impedance profile that leads to better performance is non-trivial. Here, we utilise optimal control to devise time-varying torque and stiffness profiles for highly dynamic movements in compliantly actuated robots. The proposed methodology is applied to a ballthrowing task where we demonstrate that: (i) the method is able to tailor impedance strategies to specific task objectives and system dynamics, (ii) the ability to vary stiffness leads to better performance in this class of movements, (iii) in systems with variable physical compliance, our methodology is able to exploit the energy storage capabilities of the actuators. We illustrate these in several numerical simulations, and in hardware experiments on a device with variable physical stiffness.

Exploiting variable physical damping in rapid movement tasks

Until now, design of variable physical impedance actuators (VIAs) has been limited mainly to realising variable stiffness while other components of impedance shaping, such as damping, are either fixed (e.g., with the addition of fixed passive dampers) or modulated with active feedback control schemes. In this work we introduce an actuator that is capable of simultaneous and independent physical damping and stiffness modulation. Using optimal control techniques, we explore how variable physical damping can be exploited in such an actuator in the context of rapid movement. Several numerical simulation results are presented, in addition to an experiment realised on variable impedance robotic hardware.

Transferring Human Impedance Behavior to Heterogeneous Variable Impedance Actuators

This paper presents a comparative study of approaches to control robots with variable impedance actuators (VIAs) in ways that imitate the behavior of humans. We focus on problems where impedance modulation strategies are recorded from human demonstrators for transfer to robotic systems with differing levels of heterogeneity, both in terms of the dynamics and actuation. We categorize three classes of approach that may be applied to this problem, namely, 1) direct, 2) feature-based, and 3) inverse optimal approaches to transfer. While the first is restricted to highly biomorphic plants, the latter two are shown to be sufficiently general to be applied to various VIAs in a way that is independent of the mechanical design. As instantiations of such transfer schemes, 1) a constraint-based method and 2) an apprenticeship learning framework are proposed, and their suitability to different problems in robotic imitation, in terms of efficiency, ease of use, and task performance, is characterized. The approaches are compared in simulation on systems of varying complexity, and robotic experiments are reported for transfer of behavior from human electromyographic data to two different variable passive compliance robotic devices.

Constraint-based equilibrium and stiffness control of variable stiffness actuators

Considerable research effort has gone into the design of variable passive stiffness actuators (VSAs). A number of different mechanical designs have been proposed, aimed at either a biomorphic (i.e., antagonistic) design, compactness, or simplified modelling and control. In this paper, we propose a (model-based) unified control methodology that is able to exploit the benefits of variable stiffness independent of the specifics of the mechanical design. Our approach is based on forming constraints on commands sent to the VSA to ensure that the equilibrium position and stiffness of the VSA are tracked to the desired values. We outline how our approach can be used for tracking stiffness and equilibrium position both in joint and task space, and how it may be used in the context of constrained local optimal control. In our experiments we illustrate the utility of our approach in the context of online teleoperation, to transfer compliant human behaviour to a variable stiffness device.

Optimal torque and stiffness control in compliantly actuated robots

Anthropomorphic robots that aim to approach human performance agility and efficiency are typically highly redundant not only in their kinematics but also in actuation. Variable-impedance actuators, used to drive many of these devices, are capable of modulating torque and passive impedance (stiffness and/or damping) simultaneously and independently. Here, we propose a framework for simultaneous optimisation of torque and impedance (stiffness) profiles in order to optimise task performance, tuned to the complex hardware and incorporating real-world constraints. Simulation and hardware experiments validate the viability of this approach to complex, state dependent constraints and demonstrate task performance benefits of optimal temporal impedance modulation.

Compliant actuation for energy efficient impedance modulation

Energy efficient compliant actuation is the missing ingredient and key enabler of next-generation autonomous systems, domestic robots, prosthetic devices, orthotic devices, and wearable exoskeletons, to name a few. For all these devices, one would wish to develop actuators enabling wide range impedance modulation with low energy cost. Using conventional and biologically-inspired compliant actuation, previous research led to functional devices but with high energy cost. Here we introduce a minimalistic compliant actuator to realize impedance modulation with low energy cost. Using this actuator we demonstrate stiffness augmentation in human-machine collaboration. We argue that the non-biologically-inspired actuation concept presented here may effectively complement a biological system, by restoring or extending its functionality, with negligible energy cost.

A controller for dynamic walking in bipedal robots

This paper presents an approach for the closed-loop control of actuated biped that allows natural looking and energy efficient walking. Rather than prescribe kinematic trajectories or kinematic constraints, the approach is based on the prescription of state dependent torques that “encourage” patterned movement. Some of the prescribed torques are referenced to the inertial reference frame, which largely decouples the angular dynamics of the robot, and as such greatly simplifies the selection of control parameters. Implementation of torques from the inertial coordinate frames is enabled by a joint torque computation which is motivated by Gausss principle of least constraint. The proposed approach is implemented in simulation on an anthropomorphic biped, and is shown to quickly converge to a natural looking gait limit cycle. Simulations are conducted with various control parameters and different initial conditions. The authors also show that walking speed can be altered in a simple manner by varying two intuitive controller parameters. The mechanical cost of transport computed on a representative dynamic walk is used to validate energy efficiency of the proposed control approach.