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

Walking trajectory generation & control of the humanoid robot: suralp

In recent years, the operational area of the robots started to extend and new functionalities are planned for them in our daily environments. As the human-robot interaction is being improved, the robots can provide support in elderly care, human assistance, rescue, hospital attendance and many other areas. With this motivation, an intensive research is focused around humanoid robotics in the last four decades. However, due to the nonlinear dynamics of the robot and high number of degrees of freedom, the robust balance of the bipedal walk is a challenging task. Smooth trajectory generation and online compensation methods are necessary to achieve a stable walk. In this thesis, Cartesian foot position references are generated as periodic functions with respect to a body-fixed coordinate frame. The online adjustment of these parameterized trajectories provides an opportunity in tuning the walking parameters without stopping the robot. The major contribution of this thesis in the context of trajectory generation is the smoothening of the foot trajectories and the introduction of ground push motion in the vertical direction. This pushing motion provided a dramatic improvement in the stability of the walking. Even though smooth foot reference trajectories are generated using the parameter based functions, the realization of a dynamically stable walk and maintenance of the robot balance requires walking control algorithms. This thesis introduces various control techniques to cope with disturbances or unevenness of the walking environment and compensate the mismatches between the planned and the actual walking based on sensory feedback. Moreover, an automatic homing procedure is proposed for the adjustment of the initial posture before the walking experiments. The presented control algorithms include ZMP regulation, foot orientation control, trunk orientation control, foot pitch torque difference compensation, body pitch angle correction, ground impact compensation and early landing modification. The effectiveness of the proposed trajectory generation and walking control algorithms is tested on the humanoid robot SURALP and a stable walk is achieved