Quadruped Bounding Control with Variable Duty Cycle via Vertical Impulse Scaling

This paper introduces a bounding gait control algorithm that allows a successful implementation of duty cycle modulation in the MIT Cheetah 2. Instead of controlling leg stiffness to emulate a ‘springy leg’ inspired from the Spring-Loaded-Inverted-Pendulum (SLIP) model, the algorithm prescribes vertical impulse by generating scaled ground reaction forces at each step to achieve the desired stance and total stride duration. Therefore, we can control the duty cycle: the percentage of the stance phase over the entire cycle. By prescribing the required vertical impulse of the ground reaction force at each step, the algorithm can adapt to variable duty cycles attributed to variations in running speed. Following linear momentum conservation law, in order to achieve a limit-cycle gait, the sum of all vertical ground reaction forces must match vertical momentum created by gravity during a cycle. In addition, we added a virtual compliance control in the vertical direction to enhance stability. The stiffness of the virtual compliance is selected based on the eigenvalue analysis of the linearized Poincare map and the chosen stiffness is 700 N/m, which corresponds to around 12% of the stiffness used in the previous trotting experiments of the MIT Cheetah, where the ground reaction forces are purely caused by the impedance controller with equilibrium point trajectories. This indicates that the virtual compliance control does not significantly contributes to generating ground reaction forces, but to stability. The experimental results show that the algorithm successfully prescribes the duty cycle for stable bounding gaits. This new approach can shed a light on variable speed running control algorithm.United States. Defense Advanced Research Projects Agency (M3 Program

Hierarchical controller for highly dynamic locomotion utilizing pattern modulation and impedance control : implementation on the MIT Cheetah robot

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 105-111).This thesis presents a hierarchical control algorithm for quadrupedal locomotion. We address three challenges in developing a controller for high-speed running: locomotion stability, control of ground reaction force, and coordination of four limbs. To tackle these challenges, the proposed algorithm employs three strategies. Leg impedance control provides programmable virtual compliance of each leg which achieve self-stability in locomotion. The four legs exert forces to the ground using equilibrium-point hypothesis. A gait pattern modulator imposes a desired footfall sequence. The control algorithm is verified in a dynamic simulator constructed using MATLAB and then in the subsequent experiments on the MIT Cheetah robot. The experiments on the MIT Cheetah robot demonstrates high speed trot running reaching up to the speed of 6 m/s on a treadmill. This speed corresponds to a Froude number (Fr = 7.34), which is comparatively higher than other existing quadrupedal robots.by Jongwoo Lee.S.M

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Thrust control, stabilization and energetics of a quadruped running robot

In order to achieve powered autonomous running robots it is essential to develop efficient actuator systems, especially for generating the radial thrust in the legs. In addition, the control of the radial thrust of the legs can be a simple, effective method for stabilizing the body pitch in a running gait. This paper presents the mechanical systems, models and control strategies employed to generate and control leg thrust in the KOLT quadruped running robot. An analytical model of the electro-pneumatic leg thrusting system is presented and analyzed to evaluate its performance and to facilitate the design of control strategies. Several experiments have been conducted to estimate the energy losses and determine their origins as well as to compute the energetic efficiency of the actuation system. Two thrust control methods are also proposed and tested experimentally. The closed loop method regulates thrust through the control of the hip liftoff speed, a conceptually simple control strategy that stabilizes the body pitch in pronk and trot gaits without the need for central feedback, even on irregular terrain. The open-loop control method regulates the energy added in each hop based on the model of the actuator system. The efficacy of these models and techniques is tested in several planar trot and pronk experiments, and the results are analyzed focusing on the body stabilization, the power consumption and the energetic efficiency. © SAGE Publications 2008 Los Angeles

Stance Control Inspired by Cerebellum Stabilizes Reflex-Based Locomotion on HyQ Robot

Advances in legged robotics are strongly rooted in animal observations. A clear illustration of this claim is the generalization of Central Pattern Generators (CPG), first identified in the cat spinal cord, to generate cyclic motion in robotic locomotion. Despite a global endorsement of this model, physiological and functional experiments in mammals have also indicated the presence of descending signals from the cerebellum, and reflex feedback from the lower limb sensory cells, that closely interact with CPGs. To this day, these interactions are not fully understood. In some studies, it was demonstrated that pure reflex-based locomotion in the absence of oscillatory signals could be achieved in realistic musculoskeletal simulation models or small compliant quadruped robots. At the same time, biological evidence has attested the functional role of the cerebellum for predictive control of balance and stance within mammals. In this paper, we promote both approaches and successfully apply reflex-based dynamic locomotion, coupled with a balance and gravity compensation mechanism, on the state-of-art HyQ robot. We discuss the importance of this stability module to ensure a correct foot lift-off and maintain a reliable gait. The robotic platform is further used to test two different architectural hypotheses inspired by the cerebellum. An analysis of experimental results demonstrates that the most biologically plausible alternative also leads to better results for robust locomotion

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

Robot Impedance Control and Passivity Analysis with Inner Torque and Velocity Feedback Loops

Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. Although common practice in designing nested control systems is to maximize the bandwidth of the inner loop to improve tracking performance, it may not be the most suitable approach when a certain range of impedance parameters has to be rendered. In particular, it turns out that the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g. a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.Comment: 14 pages in Control Theory and Technology (2016

On the dynamics of a quadruped robot model with impedance control: Self-stabilizing high speed trot-running and period-doubling bifurcations

The MIT Cheetah demonstrated a stable 6 m/s trot gait in the sagittal plane utilizing the self-stable characteristics of locomotion. This paper presents a numerical analysis of the behavior of a quadruped robot model with the proposed controller. We first demonstrate the existence of periodic trot gaits at various speeds and examine local orbital stability of each trajectory using Poincar`e map analysis. Beyond the local stability, we additionally demonstrate the stability of the model against large initial perturbations. Stability of trot gaits at a wide range of speed enables gradual acceleration demonstrated in this paper and a real machine. This simulation study also suggests the upper limit of the command speed that ensures stable steady-state running. As we increase the command speed, we observe series of period-doubling bifurcations, which suggests presence of chaotic dynamics beyond a certain level of command speed. Extension of this simulation analysis will provide useful guidelines for searching control parameters to further improve the system performance.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) Progra