Christophe Maufroy

2008 Special Issue: Towards a general neural controller for quadrupedal locomotion

Our study aims at the design and implementation of a general controller for quadruped locomotion, allowing the robot to use the whole range of quadrupedal gaits. The controller design phase is carried out using simulation. This paper reports the simulation of steady walking at 0.6 m/s of both the forelegs only and the hind legs only (with a supporting structure at the back and at the front respectively), achieved using our quadrupedal model.

CONCEPT AND DESIGN OF THE BIOBIPED1 ROBOT FOR HUMAN-LIKE WALKING AND RUNNING

Biomechanics research shows that the ability of the human locomotor system depends on the functionality of a highly compliant motor system that enables a variety of different motions (such as walking and running) and control paradigms (such as flexible combination of feedforward and feedback controls strategies) and reliance on stabilizing properties of compliant gaits. As a new approach of transferring this knowledge into a humanoid robot, the design and implementation of the first of a planned series of biologically inspired, compliant, and musculoskeletal robots is presented in this paper. Its three-segmented legs are actuated by compliant mono- and biarticular structures, which mimic the main nine human leg muscle groups, by applying series elastic actuation consisting of cables and springs in combination with electrical actuators. By means of this platform, we aim to transfer versatile human locomotion abilities, namely running and later on walking, into one humanoid robot design. First experimental results for passive rebound, as well as push-off with active knee and ankle joints, and synchronous and alternate hopping are described and discussed. BioBiped1 will serve for further evaluation of the validity of biomechanical concepts for humanoid locomotion.

Leg-adjustment strategies for stable running in three dimensions

The dynamics of the center of mass (CoM) in the sagittal plane in humans and animals during running is well described by the spring-loaded inverted pendulum (SLIP). With appropriate parameters, SLIP running patterns are stable, and these models can recover from perturbations without the need for corrective strategies, such as the application of additional forces. Rather, it is sufficient to adjust the leg to a fixed angle relative to the ground. In this work, we consider the extension of the SLIP to three dimensions (3D SLIP) and investigate feed-forward strategies for leg adjustment during the flight phase. As in the SLIP model, the leg is placed at a fixed angle. We extend the scope of possible reference axes from only fixed horizontal and vertical axes to include the CoM velocity vector as a movement-related reference, resulting in six leg-adjustment strategies. Only leg-adjustment strategies that include the CoM velocity vector produced stable running and large parameter domains of stability. The ability of the model to recover from perturbations along the direction of motion (directional stability) depended on the strategy for lateral leg adjustment. Specifically, asymptotic and neutral directional stability was observed for strategies based on the global reference axis and the velocity vector, respectively. Additional features of velocity-based leg adjustment are running at arbitrary low speed (kinetic energy) and the emergence of large domains of stable 3D running that are smoothly transferred to 2D SLIP stability and even to 1D SLIP hopping. One of the additional leg-adjustment strategies represented a large convex region of parameters where stable and robust hopping and running patterns exist. Therefore, this strategy is a promising candidate for implementation into engineering applications, such as robots, for instance. In a preliminary comparison, the model predictions were in good agreement with the experimental data, suggesting that the 3D SLIP is an appropriate model to describe human running in three dimensions. The prediction of stable running based on movement-related leg-adjustment strategies indicates that both humans and robots may not require external targets directing the movement to run in three dimensions based on compliant leg function. This new movement-based reference enables the control of 3D running because leg adjustment is less sensitive and gait stability is separated from directional stability.

Robust hopping based on virtual pendulum posture control

A new control approach to achieve robust hopping against perturbations in the sagittal plane is presented in this paper. In perturbed hopping, vertical body alignment has a significant role for stability. Our approach is based on the virtual pendulum concept, recently proposed, based on experimental findings in human and animal locomotion. In this concept, the ground reaction forces are pointed to a virtual support point, named virtual pivot point (VPP), during motion. This concept is employed in designing the controller to balance the trunk during the stance phase. New strategies for leg angle and length adjustment besides the virtual pendulum posture control are proposed as a unified controller. This method is investigated by applying it on an extension of the spring loaded inverted pendulum (SLIP) model. Trunk, leg mass and damping are added to the SLIP model in order to make the model more realistic. The stability is analyzed by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with a low convergence speed. To improve the performance and attain higher robustness, an event-based control of the VPP position is introduced, using feedback of the system states at apexes. Discrete linear quartic regulator is used to design the feedback controller. Considerable enhancements with respect to stability, convergence speed and robustness against perturbations and parameter changes are achieved.

Controllers for robust hopping with upright trunk based on the Virtual Pendulum concept

This paper presents a new control approach to achieve robust hopping with upright trunk in the sagittal plane. It relies on an innovative concept for trunk stabilization, called Virtual Pendulum concept, recently proposed, based on experimental finding in animal locomotion. With this concept, the trunk is stabilized by redirecting the ground reaction force to a virtual support point, named Virtual Pivot Point (VPP). This concept is combined with a new leg adjustment scheme to induce stable hopping when an extended trunk is added to SLIP model. The stability is investigated by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with low convergence speed. To improve the performances and attain higher robustness, event based control of VPP position is introduced, using feedback of the system state at apex. Dead beat control and Discrete LQR are alternatively considered to adjust the feedback gains. In both cases, considerable enhancements with respect to stability, convergence speed and robustness against perturbations are achieved.

Stable dynamic walking of a quadruped robot “Kotetsu” using phase modulations based on leg loading/unloading

In this study, we intend to show the basis of a general legged locomotion controller with the ability to integrate both posture and rhythmic motion controls and shift continuously from one control method to the other according to the walking speed. The rhythmic motion of each leg in the sagittal plane is generated by a single leg controller which controls the swing-to-stance and stance-to-swing phase transitions using respectively leg loading and unloading information. Since rolling motion induced by inverted pendulum motion during the two-legged stance phases results in the transfer of the load between the contralateral legs, leg loading/unloading involves posture information in the frontal plane. As a result of the phase modulations based on leg loading/unloading, rhythmic motion of each leg is achieved and leg coordination (resulting in a gait) emerges, even without explicit coordination among the leg controllers, allowing to realize dynamic walking in the low- to medium-speed range. But an additional ascending coordination mechanism between ipsilateral leg controllers helps to improve the stability. In this paper, we report the result of experiments using a newly constructed quadruped robot “Kotetsu” in order to verify the results of simulations. Details of trajectory generation and movies can be seen at: http://robotics.mech.kit.ac.jp/kotetsu/.

Towards a general neural controller for 3D quadrupedal locomotion

Our study aims at the design and implementation of a general controller for quadruped locomotion, allowing the robot to use the whole range of quadrupedal gaits. The controller design phase is carried out using simulation. This paper reports the simulation of steady walking at 0.6 m/s of both the forelegs only and the hind legs only (with a supporting structure at the back and at the front respectively), achieved using our quadrupedal model.

Simulation and experimental evaluation of the contribution of biarticular gastrocnemius structure to joint synchronization in human-inspired three-segmented elastic legs

The humanoid robot BioBiped2 is powered by series elastic actuators (SEA) at the leg joints. As motivated by the human muscle architecture comprising monoarticular and biarticular muscles, the SEA at joint level are supported by elastic elements spanning two joints. In this study we demonstrate in simulation and in robot experiments, to what extend synchronous joint operation can be enhanced by introducing elastic biarticular structures in the leg, reducing the risk of over-extending individual joints.

Stable dynamic walking of a quadruped via phase modulations against small disturbances

It is generally accepted that locomotion in animals is based on a trade-off between energy consumption and stability. However, this trade-off is the result of the interaction between complex mechanical and control systems. To gain insight into that issue, a step-by-step approach is needed. In this study, as a first step to investigate three dimensional quadrupedal walking, we aim at establishing a control system as “minimal” as possible, able to realize stable dynamic walk. Using a simple mechanical structure, we realized dynamic walk with a distributed control system, made of four independent leg controllers whose swing and stance phases durations are modulated based on leg loading information. Phase modulations contribute to stabilize the posture in the frontal plane via automatic duty ratios adjustments that tend to compensate perturbations of the body rolling motion. By applying lateral perturbations, we found that the control system withstands well perturbations increasing the rolling motion amplitude, but is sensible to perturbations that suddenly decrease it, as the foreleg on the more loaded side is prevented to swing. Hence, we implemented an ascending coordination mechanism where the transition to swing in a hind leg promotes the same event in the foreleg. The duration of the subsequent foreleg swing phase is reduced to prevent excessive increase of the rolling motion amplitude. The resultant control system, although extremely simple, was able to realize dynamic walk resistant to small disturbances (lateral perturbations and terrain irregularities).

Simplified control of upright walking by exploring asymmetric gaits induced by leg damping

A simple trunk stabilization strategy, called the virtual pendulum (VP) concept, was recently proposed based on human walking data. The implementation of this concept in a simulation model extending the bipedal spring-loaded inverted pendulum (BSLIP) model with a rigid trunk yielded stable upright walking and running patterns. In this study, a first step towards the transfer of the VP concept to real robotic platforms is made by investigating how energy losses due to damping along the leg axis influence the system behavior during walking. We found that the introduction of damping improves the predicted stability of the gait patterns and the robustness of the system with respect to the trunk control parameter. However, further increase of damping reduces the robustness with respect to the leg control parameters. Hence, the control of upright walking based on compliant leg function may be facilitated if an appropriate amount of leg damping is provided.