Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance

An Overview on Principles for Energy Efficient Robot Locomotion

Despite enhancements in the development of robotic systems, the energy economy of today's robots lags far behind that of biological systems. This is in particular critical for untethered legged robot locomotion. To elucidate the current stage of energy efficiency in legged robotic systems, this paper provides an overview on recent advancements in development of such platforms. The covered different perspectives include actuation, leg structure, control and locomotion principles. We review various robotic actuators exploiting compliance in series and in parallel with the drive-train to permit energy recycling during locomotion. We discuss the importance of limb segmentation under efficiency aspects and with respect to design, dynamics analysis and control of legged robots. This paper also reviews a number of control approaches allowing for energy efficient locomotion of robots by exploiting the natural dynamics of the system, and by utilizing optimal control approaches targeting locomotion expenditure. To this end, a set of locomotion principles elaborating on models for energetics, dynamics, and of the systems is studied

Resonant hopping of a robot controlled by an artificial neural oscillator

"The bouncing gaits of terrestrial animals (hopping, running, trotting) can be modeled as a hybrid dynamic system, with spring-mass dynamics during stance and ballistic motion during the aerial phase. We used a simple hopping robot controlled by an artificial neural oscillator to test the ability of the neural oscillator to adaptively drive this hybrid dynamic system. The robot had a single joint, actuated by an artificial pneumatic muscle in series with a tendon spring. We examined how the oscillator-robot system responded to variation in two neural control parameters: descending neural drive and neuromuscular gain. We also tested the ability of the oscillator-robot system to adapt to variations in mechanical properties by changing the series and parallel spring stiffnesses. Across a 100-fold variation in both supraspinal gain and muscle gain, hopping frequency changed by less than 10%. The neural oscillator consistently drove the system at the resonant half-period for the stance phase, and adapted to a new resonant half-period when the muscle series and parallel stiffnesses were altered. Passive cycling of elastic energy in the tendon accounted for 70-79% of the mechanical work done during each hop cycle. Our results demonstrate that hopping dynamics were largely determined by the intrinsic properties of the mechanical system, not the specific choice of neural oscillator parameters. The findings provide the first evidence that an artificial neural oscillator will drive a hybrid dynamic system at partial resonance."http://deepblue.lib.umich.edu/bitstream/2027.42/64204/1/bb8_2_026001.pd

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

A Dynamics and Stability Framework for Avian Jumping Take-off

Jumping take-off in birds is an explosive behaviour with the goal of providing a rapid transition from ground to airborne locomotion. An effective jump is predicated on the need to maintain dynamic stability through the acceleration phase. The present study concerns understanding how birds retain control of body attitude and trajectory during take-off. Cursory observation suggests that stability is achieved with relatively little cost. However, analysis of the problem shows that the stability margins during jumping are actually very small and that stability considerations play a significant role in selection of appropriate jumping kinematics. We use theoretical models to understand stability in prehensile take-off (from a perch) and also in non-prehensile take-off (from the ground). The primary instability is tipping, defined as rotation of the centre of gravity about the ground contact point. Tipping occurs when the centre of pressure falls outside the functional foot. A contribution of the paper is the development of graphical tipping stability margins for both centre of gravity location and acceleration angle. We show that the nose-up angular acceleration extends stability bounds forward and is hence helpful in achieving shallow take-offs. The stability margins are used to interrogate simulated take-offs of real birds using published experimental kinematic data from a guinea fowl (ground take-off) and a diamond dove (perch take-off). For the guinea fowl the initial part of the jump is stable, however simulations exhibit a stuttering instability not observed experimentally that is probably due to absence of compliance in the idealised joints. The diamond dove model confirms that the foot provides an active torque reaction during take-off, extending the range of stable jump angles by around 45{\deg}.Comment: 21 pages, 11 figures; supplementary material: https://figshare.com/s/86b12868d64828db0d5d; DOI: 10.6084/m9.figshare.721056

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019