Natural ZMP trajectories for biped robot reference generation

The control of a biped humanoid is a challenging task due to the hard-to-stabilize dynamics. Walking reference trajectory generation is a key problem. Linear Inverted Pendulum Model (LIPM) and Zero Moment Point (ZMP) Criterion based approaches in stable walking reference generation are reported. In these methods, generally, the ZMP reference during a stepping motion is kept fixed in the middle of the supporting foot sole. This kind of reference generation lacks naturalness, in that, the ZMP in the human walk does not stay fixed, but it moves forward under the supporting foot. This paper proposes a reference generation algorithm based on the LIPM and moving support foot ZMP references. The application of Fourier series approximation simplifies the solution and it generates a smooth ZMP reference. A simple inverse kinematics based joint space controller is used for the tests of the developed reference trajectory through full-dynamics 3D simulation. A 12 DOF biped robot model is used in the simulations. Simulation studies suggest that the moving ZMP references are more energy efficient than the ones with fixed ZMP under the supporting foot. The results are promising for implementations

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

Integration of vertical COM motion and angular momentum in an extended Capture Point tracking controller for bipedal walking

In this paper, we demonstrate methods for bipedal walking control based on the Capture Point (CP) methodology. In particular, we introduce a method to intuitively derive a CP reference trajectory from the next three steps and extend the linear inverted pendulum (LIP) based CP tracking controller introduced in [1], generalizing it to a model that contains vertical CoM motions and changes in angular momentum. Respecting the dynamics of general multibody systems, we propose a measurement-based compensation of multi-body effects, which leads to a stable closed-loop dynamics of bipedal walking robots. In addition we propose a ZMP projection method, which prevents the robots feet from tilting and ensures the best feasible CP tracking. The extended CP controller’s performance is validated in OpenHRP3 [2] simulations and compared to the controller proposed in [1]

Influence of frictions on gait optimization of a biped robot with an anthropomorphic knee

This paper presents the energy consumption of a biped robot with a new modelled structure of knees which is called rolling knee (RK). The dynamic model, the actuators and the friction coefficients of the gear box are known. The optimal energy consumption can also be calculated. The first part of the paper is to validate the new kinematic knee on a biped robot by comparing the energy consumption during a walking step of the identical biped but with revolute joint knees. The cyclic gait is given by a succession of Single Support Phase (SSP) followed by an impact. The gait trajectories are parameterized by cubic spline functions. The energetic criterion is minimized through optimization while using the simplex algorithm and Lagrange penalty functions to meet the constraints of stability and deflection of the mobile foot. An analysis of the friction coefficients is done by simulation to compare the human characteristics to the robot with RK. The simulation results show an energy consumption reduction through the biped with rolling knee configuration. The influence of friction coefficients shows the energy consumption of biped robot is close to that of the human.ANR-09-SEGI-011-R2A2; French National Research Agenc

Optimal Walking of an Underactuated Planar Biped with Segmented Torso

Recently, underactuated bipeds with pointed feet have been studied to achieve dynamic and energy efficient robot walking patterns. However, these studies usually simplify a robot torso as one link, which is different from a human torsos containing 33 vertebrae. In this paper, therefore, we study the optimal walking of a 6-link planar biped with a segmented torso derived from its 5-link counterpart while ensuring that two models are equivalent when the additional torso joint is locked. For the walking, we suppose that each step is composed of a single support phase and an instantaneous double support phase, and two phases are connected by a plastic impact mapping. In addition, the controlled outputs named symmetry outputs capable of generating exponentially stable orbits using hybrid zero dynamics, are adopted to improve physical interpretation. The desired outputs are parameterized by B´ezier functions, with 5-link robot having 16 parameters to optimize and 6-link robot having 19 parameters. According to our energy criterion, the segmented torso structure may reduce energy consumption up to 8% in bipedal walking, and the maximum energy saving is achieved at high walking speeds, while leaving the criteria at low walking speeds remain similar for both robots.China CSC LCF

Eligibility Propagation to Speed up Time Hopping for Reinforcement Learning

A mechanism called Eligibility Propagation is proposed to speed up the Time Hopping technique used for faster Reinforcement Learning in simulations. Eligibility Propagation provides for Time Hopping similar abilities to what eligibility traces provide for conventional Reinforcement Learning. It propagates values from one state to all of its temporal predecessors using a state transitions graph. Experiments on a simulated biped crawling robot confirm that Eligibility Propagation accelerates the learning process more than 3 times.Comment: 7 page

Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs

This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of a control Lyapunov function (CLF)-based walking controller for a biped robot. Previous work by the authors has demonstrated the effectiveness of CLF controllers for stabilizing periodic gaits for biped walkers, and the current work expands on those results by providing a more effective means for handling control saturations. The new approach, based on a convex optimization routine running at a 1 kHz control update rate, is useful not only for handling torque saturations but also for incorporating a whole family of user-defined constraints into the online computation of a CLF controller. The paper concludes with an experimental implementation of the main results on the bipedal robot MABEL