Restricted Discrete Invariance and Self-Synchronization For Stable Walking of Bipedal Robots

Models of bipedal locomotion are hybrid, with a continuous component often generated by a Lagrangian plus actuators, and a discrete component where leg transfer takes place. The discrete component typically consists of a locally embedded co-dimension one submanifold in the continuous state space of the robot, called the switching surface, and a reset map that provides a new initial condition when a solution of the continuous component intersects the switching surface. The aim of this paper is to identify a low-dimensional submanifold of the switching surface, which, when it can be rendered invariant by the closed-loop dynamics, leads to asymptotically stable periodic gaits. The paper begins this process by studying the well-known 3D Linear Inverted Pendulum (LIP) model, where analytical results are much easier to obtain. A key contribution here is the notion of \textit{self-synchronization}, which refers to the periods of the pendular motions in the sagittal and frontal planes tending to a common period. The notion of invariance resulting from the study of the 3D LIP model is then extended to a 9-DOF 3D biped. A numerical study is performed to illustrate that asymptotically stable walking may be obtained.Comment: Conferenc

Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\'e map of the hybrid zero dynamics. Three strategies are explored. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller. In the third approach, the effect of output selection is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller

Study and choice of actuation for a walking assist device

International audienceA walking assist device (WAD) with bodyweight support reduces energy expenditure of a walking person. However, it is also important that the location of actuators in the WAD will be optimally chosen. For this purpose a wearable assist device composed of a bodyweight support, legs and shoes articulated with hip (upper joint), knee (middle joint), and ankle (lower joint) is discussed. Since human walk involves large displacements only in sagittal plane, a planar model is considered. In order to evaluate the optimal distribution of input torques, a bipedal model of a seven-link system with several walking velocities is coupled with the mentioned WAD. To study the efficiency of the WAD and to choose an appropriate actuation, the torque cost is evaluated when the same walking pattern are tracked with and without a WAD. The paper deals with the torque cost for the human and the WAD with several types of actuation. It is shown that full actuation with six motors or partial actuation with two motors located at the upper joints are two more efficient solutions while an actuation at the middle joints or lower joints only is ineffective. The numerical simulations carried out for several walking velocities confirm the mentioned observations

Compliant Joints Increase the Energy Efficiency of Bipedal Robot

6International audienceThe energetic effects of knee locking and addition of linear elastic members to different joints of a seven-link fully actuated planar bipedal robot were studied. The focus was on the reduction of energy consumption during walking. An impactless walking gait was studied and the energetic cost of walking was determined without joint stiffness and knee locking as a baseline for comparison. The gait trajectory was then optimized by adding spring to different joints, energetic cost of walk was then calculated at different walking speeds. Support knee was then mechanically locked and gait was optimized to find the cost of walking. The energetic cost of walking determined for the above two cases was then compared to the baseline cost. It was observed that addition of torsional springs at both knees can reduce the walking cost up to 62% at lower speeds and both hips up to 35% at high walking speeds with spring stiffness as an optimization parameter for both cases. Mechanically locking the support knee can reduce the cost of walking up to 84% at slow walking speeds with gait and knee locking angle optimized

How to build web self-services by functional profiles?

International audienceCompanies, institutions, and local authorities seek to computerize services to be more profitable in terms of productivity, profitability, quality of service, traceability... The main issues are the identification of problems to solve and the choice of adapted solutions. To build these solutions, functional and technical profiles must communicate to understand precisely the domain, the problem, and the expected features... This paper provides a framework composed of three contributions, which aim to simplify the building of web self-services by functional profiles. The first part deals with a language to specify functional needs using the main concept of goal. This language must be as simple as possible but not limiting. The second part deals with the tool to use this language and, finally, the last section is a set of interpretations to simplify communication between all involved people. To automate a large part of recurrent tasks, all the proposed approach complies with model driven methodology

Online adaptation of reference trajectories for the control of walking systems

International audienceA simple and widely used way to make a robotic system walk without falling is to make it track a reference tra jectory in one way or another, but the stability obtained this way may be limited and even small perturbations may lead to a fall. We propose here a series of heuristics to improve the stability that can be obtained from such a tracking control law, through an online adaptation of the choice of the reference tra jectory being tracked. Encouraging simulations are obtained in the end on a simple planar biped model

Finite Time Stabilization of a Double Integrator - Part I: Continuous Sliding Mode-based Position Feedback Synthesis

International audienceThe twisting and supertwisting algorithms, generating important classes of second order sliding modes (SOSM's), are well-recognized for their finite time stability and robustness properties. In the present paper, a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of SOSM's that present the aforementioned attractive features. Thus modified, the twisting and supertwisting algorithms are utilized in the state feedback synthesis and, respectively, velocity observer design, made for the finite time stabilization of a double integrator if only position measurements are available. Performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations

Synthesis of an electric sensor based control for underwater multi-agents navigation in a file

International audienceThanks to an electro-sensible skin, some species of fish can feel the surrounding electric field generated by them-self or other fish. Known under the name of "electric-sense", this ability allows these fish to navigate in confined surroundings. Based on a bio-inspired electric sensor, this article presents how this electric sense can be used for the navigation in formation of several underwater vehicles. The formation considered is a file, each vehicle is assumed to follow its predecessor at a given distance. In confined environment, the file formation is interesting since fish can follow the same safe path. Being based on the servoing of the electric measurements, these laws do not require the knowledge of the location of the agents. The underwater vehicle studied have non holonomic properties, their forward velocity has no lateral component. Depending on the choice of the controlled outputs (combination of electric measures) we will see that path followed by the follower agents can be different and a methodology to choose the output will be defined in order that all the agents follow the leader path in presence of curved motion of the leader. The influence of the number of electrodes is discussed. Simulation results illustrate the proposed approach

Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters