Salman Faraji

Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

In this paper, we formulate a novel hierarchical controller for walking of torque controlled humanoid robots. Our method uses a whole body optimization approach which generates joint torques, given Cartesian accelerations of different points on the robot. Over such variable translation, we can plan our desired foot trajectories in Cartesian space between starting and ending positions of the foot on the ground. On top level, we use the simplified Linear Inverted Pendulum Model to predict the future motion of the robot. With LIPM, we derive a formulation where the whole system is described by the state of center of mass and footstep locations serve as discrete inputs to this linear system. We then use model predictive control to plan optimal future footsteps which resemble a reference plan, given desired sagittal and steering velocities determined by the high-end user. Using simulations on a kid-size torque controlled humanoid robot, the method tolerates various disturbances such as external pushes, sensor noises, model errors and delayed communication in the control loop. It can perform robust walking over slopes and uneven terrains blindly and turn rapidly at the same time. Our generic dynamics model-based method does not depend on any off-line optimization, being suitable for typical torque controlled humanoid robots.

Versatile and robust 3D walking with a simulated humanoid robot (Atlas): A model predictive control approach

In this paper, we propose a novel walking method for torque controlled robots. The method is able to produce a wide range of speeds without requiring off-line optimizations and re-tuning of parameters. We use a quadratic whole-body optimization method running online which generates joint torques, given desired Cartesian accelerations of center of mass and feet. Using a dynamics model of the robot inside this optimizer, we ensure both compliance and tracking, required for fast locomotion. We have designed a foot-step planner that uses a linear inverted pendulum as simplified robot internal model. This planner is formulated as a quadratic convex problem which optimizes future steps of the robot. Fast libraries help us performing these calculations online. With very few parameters to tune and no perception, our method shows notable robustness against strong external pushes, relatively large terrain variations, internal noises, model errors and also delayed communication.

The effect of fractionality nature in differences between computer simulation and experimental results of a chaotic circuit

In practice, some differences are usually observed between computer simulation and experimental results of a chaotic circuit. In this paper, it is tried to obtain computer simulation results having more correlation with those obtained in practice by using more realistic models for chaotic circuits. This goal is achieved by considering the fractionality nature of electrical capacitors in the model of a chaotic circuit.

Practical considerations in using inverse dynamics on a humanoid robot: Torque tracking, sensor fusion and Cartesian control laws

Although considering dynamics in the control of humanoid robots can improve tracking and compliance in agile tasks, it requires local and global states of the system, precise torque control and proper modeling. In this paper we discuss practical issues to implement inverse dynamics on a torque controlled robot. By modeling electrical actuators offline, inverting such model and estimating the friction on-line, a high bandwidth torque controller is implemented. In addition, a cascade of optimization problems to fuse all the sensory data coming from IMU, joint encoders and contact force sensors estimate the robots global state robustly. Our estimation builds the kinematic chain of the legs from the center of pressure which is more robust in case of slight slippage, tilting or rolling of the feet. Thanks to precise and fast torque control, robust state estimation and optimization-based whole body inverse dynamics, the real robot can keep balance with very small stiffness and damping in Cartesian space. It can also recover from strong pushes and perform dexterous tasks. The highly compliant and stable performance is based on pure torque control, without any joint damping or position/velocity tracking.

Compliant and adaptive control of a planar monopod hopper in rough terrain

In this paper, a method is proposed for controlling a hopping monopod. It takes dynamics of the robot into account to have better nominal tracking of desired trajectories and more compliant environmental interactions at the same time. We have incorporated also natural dynamics of the robot into the system by using off-line gaits extracted from optimizations on energy. The main control loop consists of the projected inverse dynamics that generates actuator torques given desired trajectories and also a feedback loop designed and tuned specifically for the structure of the robot. A trajectory generator uses known optimal trajectories together with some stabilizing control laws that modify these trajectories to have better robustness in different situations. The average speed of the robot is also regulated by means of a self-organizing controller. We apply soft transitions in trajectories from phase to phase to avoid sharp actuator input profiles. Our method is successfully tested on a monopod hopper robot in simulation. It can handle slightly rough or sloped terrains while maintaining a given average speed. Simulation results suggest that our method is a promising candidate to control a real robot under construction.

3LP: a linear 3D-walking model including torso and swing dynamics

In this paper, we present a new mechanical model for biped locomotion, composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to a double support phase, this model has different actuation possibilities in the swing hip and stance ankle which produce a broad range of walking gaits. Without the need for numerical time-integration, closed form solutions help to find periodic gaits which could simply scale in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can potentially provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such a property comes from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract template space. The proposed model produces human-like torque and ground reaction force profiles, and thus, compared to point-mass models, it is more promising for the generation of dynamic walking trajectories. Despite being linear and lacking many features of human walking like center of mass excursion, knee flexion and ground clearance, we show that the proposed model can explain one of the main optimality trends in human walking, i.e. the nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis remains for future works.

Finding Proper Configurations for Modular Robots by Using Genetic Algorithm on Different Terrains

This paper presents a novel self-reconfigurable robotic system named ACMoD where each module can move itself individually. It can also attach to other modules to build various configurations and change this configuration adaptively on different terrains. In this paper, we have proposed Genetic Algorithm for optimizing the path of modular robots through a static grid of different terrain blocks. Each chromosome consists of path and modular robot configurations. Solution of the proposed algorithm is a proper path and configuration pattern for crossing the environment with minimum effort related to a pre-defined multi-objective function. Finally, for investigating the efficiency of the proposed algorithm, the performance of proposed algorithm is compared to Dijkstra algorithm in different environments.

Singularity-Tolerant Inverse Kinematics for Bipedal Robots: An Efficient Use of Computational Power to Reduce Energy Consumption

We propose a nonlinear inverse kinematics formulation which solves for positions directly. Compared to various other popular methods that integrate velocities, this formulation can better handle fast, asymmetric, and singular-postured balancing tasks for humanoid robots. We also introduce joint position and velocity boundaries as inequality constraints in the optimization to ensure feasibility. Such boundaries provide safety when approaching or getting away from joint limits or singularities. Besides, mixing positions and velocities in our proposed algorithm facilitates recovery from singularities, which is very difficult for conventional inverse kinematics methods. Extensive demonstrations on the real robot prove the applicability of the proposed algorithm while improving power consumption. Our formulation automatically handles different numerical and behavioral difficulties rising from singularities, which makes it a reliable low-level conversion block for different Cartesian planners.

Modeling Robot Geometries Like Molecules, Application to Fast Multicontact Posture Planning for Humanoids

Traditional joint-space models used to describe equations of motion for humanoid robots offer nice properties linked directly to the way these robots are built. However, from a computational point of view and convergence properties, these models are not the fastest when used in planning optimizations. In this letter, inspired by Cartesian coordinates used to model molecular structures, we propose a new modeling technique for humanoid robots. We represent robot segments by vectors and derive equations of motion for the full body. Using this methodology in a complex task of multicontact posture planning with minimal joint torques, we set up optimization problems and analyze the performance. We demonstrate that compared to joint-space models that get trapped in local minima, the proposed vector-based model offers much faster computational speed and a suboptimal but unique final solution. The underlying principle lies in reducing the nonlinearity and exploiting the sparsity in the problem structure. Apart from the specific case study of posture optimization, these principles can make the proposed technique a promising candidate for many other optimization-based complex tasks in robotics.

A simple model of mechanical effects to estimate metabolic cost of human walking

Since the advent of energy measurement devices, gait experiments have shown that energetic economy has a large influence on human walking behavior. However, few cost models have attempted to capture the major energy components under comprehensive walking conditions. Here we present a simple but unified model that uses walking mechanics to estimate metabolic cost at different speeds and step lengths and for six other biomechanically-relevant gait experiments in literature. This includes at various gait postures (e.g. extra foot lift), anthropometric dimensions (e.g. added mass), and reduced gravity conditions, without the need for parameter tuning to design new gait trajectories. Our results suggest that the metabolic cost of walking can largely be explained by the linear combination of four costs—swing and torso dynamics, center of mass velocity redirection, ground clearance, and body weight support. The overall energetic cost is a tradeoff among these separable components, shaped by how they manifest under different walking conditions.