Trajectory generation for continuous leg forces during double support and heel-to-toe shift based on divergent component of motion

This paper works with the concept of Divergent Component of Motion (DCM), also called ’(instantaneous) Capture Point’. We present two real-time DCM trajectory generators for uneven (three-dimensional) ground surfaces, which lead to continuous leg (and corresponding ground reaction) force profiles and facilitate the use of toe-off motion during double support. Thus, the resulting DCM trajectories are well suited for real-world robots and allow for increased step length and step height. The performance of the proposed methods was tested in numerous simulations and experiments on IHMC’s Atlas robot and DLR’s humanoid robot TORO

Straight-Leg Walking Through Underconstrained Whole-Body Control

We present an approach for achieving a natural, efficient gait on bipedal robots using straightened legs and toe-off. Our algorithm avoids complex height planning by allowing a whole-body controller to determine the straightest possible leg configuration at run-time. The controller solutions are biased towards a straight leg configuration by projecting leg joint angle objectives into the null-space of the other quadratic program motion objectives. To allow the legs to remain straight throughout the gait, toe-off was utilized to increase the kinematic reachability of the legs. The toe-off motion is achieved through underconstraining the foot position, allowing it to emerge naturally. We applied this approach of under-specifying the motion objectives to the Atlas humanoid, allowing it to walk over a variety of terrain. We present both experimental and simulation results and discuss performance limitations and potential improvements.Comment: Submitted to 2018 IEEE International Conference on Robotics and Automatio

Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional "ankle strategy" balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements

3D locomotion based on Divergent Component of Motion

Two-page abstract of a talk about the extension of the concept of Divergent Component of Motion (a.k.a. "Capture Point") to 3D

A Benchmarking of DCM Based Architectures for Position and Velocity Controlled Walking of Humanoid Robots

This paper contributes towards the development and comparison of Divergent-Component-of-Motion (DCM) based control architectures for humanoid robot locomotion. More precisely, we present and compare several DCM based implementations of a three layer control architecture. From top to bottom, these three layers are here called: trajectory optimization, simplified model control, and whole-body QP control. All layers use the DCM concept to generate references for the layer below. For the simplified model control layer, we present and compare both instantaneous and Receding Horizon Control controllers. For the whole-body QP control layer, we present and compare controllers for position and velocity control robots. Experimental results are carried out on the one-meter tall iCub humanoid robot. We show which implementation of the above control architecture allows the robot to achieve a walking velocity of 0.41 meters per second.Comment: Submitted to Humanoids201

A Hybrid Planning and Control Model for Biped Feet Rotation

This thesis proposes methods for biped walking locomotion with feet rotation. The chief objective of this work is to first generate a guide trajectory based on designing a zero moment point (ZMP) trajectory within the support polygon and obtain linear controlling methods to stabilize the walking procedure with feet rotation. With feet rotation, the walking procedure will be more humanlike, more flexible and possible saving energy. However, when the feet are rotating around their edge, either toe or heel, the entire robot is under-actuated which are more difficult to control. By using preview control, a dynamic model of the system can be derived to control the robot. This thesis is based upon a simplified model of the Reemc Robot by PAL Robotics. The simplified model has fixed arms, since only leg motions are considered, and two legs. Each leg has three degrees of freedom. The robot is presented as a three mass model. A guided gait trajectory is first generated as the boundary condition for the ZMP. Interpolation methods are used to generate a ZMP trajectory from a set of discrete points that stay inside the boundary condition. By designing the transition model from single support phase and double support phase, a general schema can be achieved. Following the assumptions of a linear inverted pendulum, trajectories of all three masses can be solved. Inverse kinematics can now give the reference joint trajectories, which, together with the reference ZMP trajectory, is used in control methods to minimize the error between the reference trajectory and actual trajectory in simulation. Control methods are used to stabilize the motion of the walking procedure. Preview control is used for the single support phase where the behavior of all three masses is linear. A proper input can be obtained through optimization. During the double support phase, the feet rotations are nonlinear and under-actuated since the feet are rotating around their edge where no torque can be produced from the ground. By using preview control, an input can be applied to the robot so that the robot can maintain dynamic stability.Ope

Investigation of Optimization Targets for Predictive Simulation of Human Gait with Model Predictive Control

The design and development of gait-related treatments and devices is inhibited by anabsence of predictive gait models. Understanding of human gait and what motivates walkingpatterns is still limited, despite walking being one of the most routine human activities. While asignificant body of literature exists on gait modeling and optimization criteria to achievesimulated, normal gait, particularly with neuromuscular models, few studies have aimed to applyoptimization targets which approximate metabolic cost to mechanical gait models. Even fewerhave attempted this predictively, with no joint angle data specified a priori. The Sunmodel [31], [32] is one such mechanical framework which utilizes MPC to predict the dynamics ofhuman walking. This thesis expands the Sun model [31], [32] to simulate a full gait cycle (CG) andinvestigates the application of new optimization targets within an existing Model PredictiveControl (MPC) framework for predictive gait simulation developed by Sun [31], [32] .The Sun model [31], [32] was previously limited to a half gait cycle (GC) which assumedbilateral symmetry and optimized only according to characteristic constraints such as step lengthand velocity of the center of mass (COM). In this thesis, the Sun framework and MPC controlscheme were expanded to generate consecutive double support (DS), single support (SS), DS, andSS period simulations, which constitutes a full GC. The resulting GC simulation was not markedby GC events toe off (TO) and heel strike (HS), but did achieve continuity over the period whichwas not achieved by the Sun model [31], [32] . Additionally, new cost functions were developedconsistent with existing literature which suggests that the Central Nervous System (CNS) uses avariety of energy-related targets in generating gait. This thesis demonstrates that the applicationof optimization targets which approximate metabolic costs is possible with the proposed MPCframework for a mechanical gait model, but that the performance of resulting simulations shouldnot be evaluated until a full GC marked by TO and HS is achieved.While a continuous full GC simulation was achieved, the failure of the model to reliablymeet characteristic constraints, particularly in SS, prevents simulation of a GC marked by TO andHS. The work in this thesis points primarily to the failure of the optimization routine within theMPC framework to reliably find a solution that meets constraints as the cause of this problem. Ifthe optimization problem can be classified, an appropriate solution algorithm could be chosenwhich could reliably find a solution for any given set of constraints and initial conditions (IC).Identifying an appropriate solution algorithm could make the MPC framework proposed a viablemethod of gait prediction and simulation.This investigation provides researchers better understanding of the application ofenergy-based optimization in mechanical gait models and the current limitations of gaitprediction and simulation. In addition, direction is given to the future work necessary to establishMPC as a viable control method for gait simulation

Unified Motion Planner for Walking, Running, and Jumping Using the Three-Dimensional Divergent Component of Motion

Running and jumping are locomotion modes that allow legged robots to rapidly traverse great distances and overcome difficult terrain. In this article, we show that the 3-D divergent component of motion (3D-DCM) framework, which was successfully used for generating walking trajectories in previous works, retains its validity and coherence during flight phases, and, therefore, can be used for planning running and jumping motions. We propose a highly efficient motion planner that generates stable center-of-mass (CoM) trajectories for running and jumping with arbitrary contact sequences and time parametrizations. The proposed planner constructs the complete motion plan as a sequence of motion phases that can be of different types: stance, flight, transition phases, etc. We introduce a unified formulation of the CoM and DCM waypoints at the start and end of each motion phase, which makes the framework extensible and enables the efficient waypoint computation in matrix and algorithmic form. The feasibility of the generated reference trajectories is demonstrated by extensive whole-body simulations with the humanoid robot TORO