ZMP Constraint Restriction for Robust Gait Generation in Humanoids

We present an extension of our previously proposed IS-MPC method for humanoid gait generation aimed at obtaining robust performance in the presence of disturbances. The considered disturbance signals vary in a range of known amplitude around a mid-range value that can change at each sampling time, but whose current value is assumed to be available. The method consists in modifying the stability constraint that is at the core of IS-MPC by incorporating the current mid-range disturbance, and performing an appropriate restriction of the ZMP constraint in the control horizon on the basis of the range amplitude of the disturbance. We derive explicit conditions for recursive feasibility and internal stability of the IS-MPC method with constraint modification. Finally, we illustrate its superior performance with respect to the nominal version by performing dynamic simulations on the NAO robot

On the design of a nonlinear model predictive controller based on enhanced disturbance observer for dynamic walking of biped robots

In this paper a nonlinear model predictive control strategy based on enhanced nonlinear disturbance observer is proposed to control the dynamic walking of biped robots on the smooth surface considering double support phase, single support phase, and impact. Optimal tracking of reference trajectories via optimal joint torque is established via a nonlinear predictive controller with well-defined cost functions and associated constraints. The implementation of a conventional disturbance observer encounters numerous challenges due to the joint acceleration requirements. The proposed nonlinear disturbance observer here, which only requires the position and angular velocity, helps to estimate the disturbances introduced on the robot and reduce the complications. The simulation results performed on the dynamic walking of a 5-DOF biped robot on flat surface shows the merits of the proposed method in tracking arbitrary trajectories despite the disturbances

From walking to running: robust and 3D humanoid gait generation via MPC

Humanoid robots are platforms that can succeed in tasks conceived for humans. From locomotion in unstructured environments, to driving cars, or working in industrial plants, these robots have a potential that is yet to be disclosed in systematic every-day-life applications. Such a perspective, however, is opposed by the need of solving complex engineering problems under the hardware and software point of view. In this thesis, we focus on the software side of the problem, and in particular on locomotion control. The operativity of a legged humanoid is subordinate to its capability of realizing a reliable locomotion. In many settings, perturbations may undermine the balance and make the robot fall. Moreover, complex and dynamic motions might be required by the context, as for instance it could be needed to start running or climbing stairs to achieve a certain location in the shortest time. We present gait generation schemes based on Model Predictive Control (MPC) that tackle both the problem of robustness and tridimensional dynamic motions. The proposed control schemes adopt the typical paradigm of centroidal MPC for reference motion generation, enforcing dynamic balance through the Zero Moment Point condition, plus a whole-body controller that maps the generated trajectories to joint commands. Each of the described predictive controllers also feature a so-called stability constraint, preventing the generation of diverging Center of Mass trajectories with respect to the Zero Moment Point. Robustness is addressed by modeling the humanoid as a Linear Inverted Pendulum and devising two types of strategies. For persistent perturbations, a way to use a disturbance observer and a technique for constraint tightening (to ensure robust constraint satisfaction) are presented. In the case of impulsive pushes instead, techniques for footstep and timing adaptation are introduced. The underlying approach is to interpret robustness as a MPC feasibility problem, thus aiming at ensuring the existence of a solution for the constrained optimization problem to be solved at each iteration in spite of the perturbations. This perspective allows to devise simple solutions to complex problems, favoring a reliable real-time implementation. For the tridimensional locomotion, on the other hand, the humanoid is modeled as a Variable Height Inverted Pendulum. Based on it, a two stage MPC is introduced with particular emphasis on the implementation of the stability constraint. The overall result is a gait generation scheme that allows the robot to overcome relatively complex environments constituted by a non-flat terrain, with also the capability of realizing running gaits. The proposed methods are validated in different settings: from conceptual simulations in Matlab to validations in the DART dynamic environment, up to experimental tests on the NAO and the OP3 platforms