Abstract-In this paper, we formulate a novel hierarchical controller for walking of torque controlled humanoid robots. Our method uses an online 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 child-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.

Abstract-In this paper, we present a new model of biped locomotion which is 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 double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can 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 property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level 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 precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speedfrequency 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 still remain for future works.

Despite enhancements in the development of robotic systems, the energy economy of today's robots lags far behind that of biological systems. This is in particular critical for untethered legged robot locomotion. To elucidate the current stage of energy efficiency in legged robotic systems, this paper provides an overview on recent advancements in development of such platforms. The covered different perspectives include actuation, leg structure, control and locomotion principles. We review various robotic actuators exploiting compliance in series and in parallel with the drive-train to permit energy recycling during locomotion. We discuss the importance of limb segmentation under efficiency aspects and with respect to design, dynamics analysis and control of legged robots. This paper also reviews a number of control approaches allowing for energy efficient locomotion of robots by exploiting the natural dynamics of the system, and by utilizing optimal control approaches targeting locomotion expenditure. To this end, a set of locomotion principles elaborating on models for energetics, dynamics, and of the systems is studied.

Abstract-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 retuning 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.

Abstract-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 robot's 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.

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.

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.

Abstract-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.