Robust Cascade Controller for Nonlinearly Actuated Biped Robots: Experimental Evaluation

In this paper we consider the postural stability problem for nonlinearly actuated quasi-static biped robots, both with respect to the joint angular positions and also with reference to the gripping effect between the foot/feet against the ground during robot locomotion. Zero moment point based mathematical models are developed to establish a relationship between the robot state variables and the stability margin of the foot (feet) contact surface and the supporting ground. Then, in correspondence with the developed dynamical model and its associated uncertainty, and in the presence of non-modeled robot mechanical structure vibration modes, we propose a robust control architecture that uses two cascade regulators. The overall robust control system consists of a nonlinear robust variable structure controller in an inner feedback loop for joint trajectory tracking, and anH∞ linear robust regulator in an outer, direct zero moment point feedback loop to ensure the foot-ground contact stability. The effectiveness of this cascade controller is evaluated using a simplified prototype of a nonlinearly actuated biped robot in double support placed on top of a one-degree-of-freedom mobile platform and subjected to external disturbances. The achieved experimental results have revealed that the simplified prototype is successfully stabilized.In this paper we consider the postural stability problem for nonlinearly actuated quasi-static biped robots, both with respect to the joint angular positions and also with reference to the gripping effect between the foot/feet against the ground during robot locomotion. Zero moment point based mathematical models are developed to establish a relationship between the robot state variables and the stability margin of the foot (feet) contact surface and the supporting ground. Then, in correspondence with the developed dynamical model and its associated uncertainty, and in the presence of non-modeled robot mechanical structure vibration modes, we propose a robust control architecture that uses two cascade regulators. The overall robust control system consists of a nonlinear robust variable structure controller in an inner feedback loop for joint trajectory tracking, and anH∞ linear robust regulator in an outer, direct zero moment point feedback loop to ensure the foot-ground contact stability. The effectiveness of this cascade controller is evaluated using a simplified prototype of a nonlinearly actuated biped robot in double support placed on top of a one-degree-of-freedom mobile platform and subjected to external disturbances. The achieved experimental results have revealed that the simplified prototype is successfully stabilized

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

Ground reaction force sensor fault detection and recovery method based on virtual force sensor for walking biped robots

This paper presents a novel method for ground force sensor faults detection and faulty signal reconstruction using Virtual force Sensor (VFS) for slow walking bipeds. The design structure of the VFS consists of two steps, the total ground reaction force (GRF) and its location estimation for each leg based on the center of mass (CoM) position, the leg kinematics, and the IMU readings is carried on in the first step. In the second step, the optimal estimation of the distributed reaction forces at the contact points in the feet sole of walking biped is carried on. For the optimal estimation, a constraint model is obtained for the distributed reaction forces at the contact points and the quadratic programming optimization method is used to solve for the GRF. The output of the VFS is used for fault detection and recovery. A faulty signal model is formed to detect the faults based on a threshold, and recover the signal using the VFS outputs. The sensor offset, drift, and frozen output faults are studied and tested. The proposed method detects and estimates the faults and recovers the faulty signal smoothly. The validity of the proposed estimation method was confirmed by simulations on 3D dynamics model of the humanoid robot SURALP while walking. The results are promising and prove themselves well in all of the studied fault cases

Simple virtual slip force sensor for walking biped robots

This paper presents a novel simple Virtual Slip Force Sensor (VSFS) for a walking biped. Bipeds walking stability is critical and they tend to lose it easily in real environments. Among the significant aspects that affect the stability is the availability of the required friction force which is necessary for the robot not to slip. In this paper we propose the use of the virtual sensor to detect the slip force. The design structure of the VSFS consists of two steps, in the first step it utilizes the measured acceleration of the center of mass (CoM) and the ZMP signals in the simple linear inverted pendulum model (LIPM) to estimate the position of the CoM, and in the second step the Newton law is employed to find the total ground reaction force (GRF) for each leg based on the position of CoM. Then both the estimated force and the measured force from the sensors assembled at the foot are used to detect the slip force. The validity of the proposed estimation method was confirmed by simulations on 3D dynamics model of the humanoid robot SURALP while walking. The results are promising and prove themselves well

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

Humanoid robot walking control on inclined planes

The humanoid bipedal structure is suitable for a assitive robot functioning in the human environment. However, the bipedal walk is a difficult control problem. Walking just on even floor is not satisfactory for the applicability of a humanoid robot. This paper presents a study on bipedal walk on inclined planes. A Zero Moment Point (ZMP) based reference generation technique is employed. The orientation of the feet is adjusted online by a fuzzy logic system to adapt to different walking surface slopes. This system uses a sampling time larger than the one of the joint space position controllers. The average value of the body pitch angle is used as the inputs to the fuzzy logic system. A foot pitch orientation compensator implemented independently for the two feet complements the fuzyy controller. A 12-degrees-of-freedom (DOF) biped robot model is used in the full-dynamics 3-D simulations. Simulations are carried out on even floor and inclined planes with different slopes. The results indicate that the control method presented is successful in enabling the robot to climb slopes of 8.5 degrees (15 percent grade)

Trajectory generation with natural ZMP references for the biped walking robot SURALP

Bipedal locomotion has good obstacle avoidance properties. A robot with human appearance has advantages in human-robot communication. However, walking control is difficult due to the complex robot dynamics involved. Stable reference generation is significant in walking control. The Linear Inverted Pendulum Model (LIPM) and the Zero Moment Point (ZMP) criterion are applied in a number of studies for stable walking reference generation of biped robots. This is the main route of reference generation in this paper too. We employ a natural and continuous ZMP reference trajectory for a stable and human-like walk. The ZMP reference trajectories move forward under the sole of the support foot when the robot body is supported by a single leg. Robot center of mass (CoM) trajectory is obtained from predefined ZMP reference trajectories by Fourier series approximation. We reported simulation results with this algorithm in our previous works. This paper presents the first experimental results. Also the use of a ground push phase before foot take-offs reported in our previous works is tested first time together with our ZMP based reference trajectory. The reference generation strategy is tested via walking experiments on the 29 degrees-of-freedom (DOF) human sized full body humanoid robot SURALP (Sabanci University Robotics Research Laboratory Platform). Experiments indicate that the proposed reference trajectory generation technique is successful