Humanoid gait generation via MPC: stability, robustness and extensions

Research on humanoid robots has made significant progress in recent years, and Model Predictive Control (MPC) has seen great applicability as a technique for gait generation. The main advantages of MPC are the possibility of enforcing constraints on state and inputs, and the constant replanning which grants a degree of robustness. This thesis describes a framework based on MPC for humanoid gait generation, and analyzes some theoretical aspects which have often been neglected. In particular, the stability of the controller is proved. Due to the presence of constraints, this requires proving recursive feasibility, i.e., that the algorithm is able to recursively guarantee that a solution satisfying the constraints is found. The scheme is referred to as Intrinsically Stable MPC (IS-MPC). A basic scheme is presented, and its stability and feasibility guarantees are discussed. Then, several extensions are introduced. The guarantees of the basic scheme are carried over to a robust version of IS-MPC. Furthermore, extension to uneven ground and to a more accurate multi-mass model are discussed. Experiments on two robotic platforms (the humanoid robots HRP-4 and NAO) are presented in the concluding section

Gait generation via intrinsically stable MPC for a multi-mass humanoid model

We consider the problem of generating a gait with no a priori assigned footsteps while taking into account the contribution of the swinging leg to the total Zero Moment Point (ZMP). This is achieved by considering a multi-mass model of the humanoid and distinguishing between secondary masses with known pre-defined motion and the remaining, primary, masses. In the case of a single primary mass with constant height, it is possible to transform the original gait generation problem for the multi-mass system into a single LIP-like problem. We can then take full advantage of an intrinsically stable MPC framework to generate a gait that takes into account the swinging leg motion

MPC-based humanoid pursuit-evasion in the presence of obstacles

We consider a pursuit-evasion problem between humanoids in the presence of obstacles. In our scenario, the pursuer enters the safety area of the evader headed for collision, while the latter executes a fast evasive motion. Control schemes are designed for both the pursuer and the evader. They are structurally identical, although the objectives are different: the pursuer tries to align its direction of motion with the line- of-sight to the evader, whereas the evader tries to move in a direction orthogonal to the line-of-sight to the pursuer. At the core of the control architecture is a Model Predictive Control scheme for generating a stable gait. This allows for the inclusion of workspace obstacles, which we take into account at two levels: during the determination of the footsteps orientation and as an explicit MPC constraint. We illustrate the results with simulations on NAO humanoids

Learning Model Predictive Control for Periodic Repetitive Tasks

We propose a reference-free learning model predictive controller for periodic repetitive tasks. We consider a problem in which dynamics, constraints and stage cost are periodically time-varying. The controller uses the closed-loop data to construct a time-varying terminal set and a time-varying terminal cost. We show that the proposed strategy in closed-loop with linear and nonlinear systems guarantees recursive constraints satisfaction, non-increasing open-loop cost, and that the open-loop and closed-loop cost are the same at convergence. Simulations are presented for different repetitive tasks, both for linear and nonlinear systems.Comment: 2020 European Control Conference, Saint Petersburg, Russia. Extended version of the conference pape

Humanoid gait generation for walk-to locomotion using single-stage MPC

We consider the problem of gait generation for a humanoid robot that must walk to an assigned Cartesian goal. As a first solution, we consider a rather straightforward adaptation of our previous work: An external block produces high-level velocities, which are then tracked by a double-stage intrinsically stable MPC scheme where the orientation of the footsteps is chosen before determining their location and the CoM trajectory. The second solution, which represents the main contribution of the paper, is conceptually different: no high-level velocity is generated, and footstep orientations are chosen at the same time of the other decision variables in a singlestage MPC. This is made possible by carefully redesigning the motion constraints so as to preserve linearity. Preliminary results on a simulated NAO confirm that the single-stage method outperforms the conventional double-stage scheme

Feasibility-Driven Step Timing Adaptation for Robust MPC-Based Gait Generation in Humanoids

The feasibility region of a Model Predictive Control (MPC) algorithm is the subset of the state space in which the constrained optimization problem to be solved is feasible. In our recent Intrinsically Stable MPC (IS-MPC) method for humanoid gait generation, feasibility means being able to satisfy the dynamic balance condition, the kinematic constraints on footsteps as well as an explicit stability condition. Here, we exploit the feasibility concept to build a step timing adapter that, at each control cycle, modifies the duration of the current step whenever a feasibility loss is imminent due, e.g., to an external perturbation. The proposed approach allows the IS-MPC algorithm to maintain its linearity and adds a negligible computational burden to the overall scheme. Simulations and experimental results where the robot is pushed while walking showcase the performance of the proposed approach

Robust MPC-Based Gait Generation in Humanoids

We introduce a robust gait generation framework for humanoid robots based on our Intrinsically Stable Model Predictive Control (IS-MPC) scheme, which features a stability constraint to guarantee internal stability. With respect to the original version, the new framework adds multiple components addressing the robustness problem from different angles: an observer-based disturbance compensation mechanism; a ZMP constraint restriction that provides robustness with respect to bounded disturbances; and a step timing adaptation module to prevent the loss of feasibility. Simulation and experimental results are presented

Real-time pursuit-evasion with humanoid robots

We consider a pursuit-evasion problem between humanoids. In our scenario, the pursuer enters the safety area of the evader headed for collision, while the latter executes a fast evasive motion. Control schemes are designed for both the pursuer and the evader. They are structurally identical, although the objectives are different: the pursuer tries to align its direction of motion with the line-of-sight to the evader, whereas the evader tries to move in a direction orthogonal to the line-of-sight to the pursuer. At the core of the control scheme is a maneuver planning module which makes use of closed- form expressions exclusively. This allows its use in a replanning framework, where each robot updates its motion plan upon completion of a step to account for the perceived motion of the other. Simulation and experimental results on NAO humanoids reveal an interesting asymptotic behavior which was predicted using unicycle as template models for trajectory generation

Real-time pursuit-evasion with humanoid robots

We consider a pursuit-evasion problem between humanoids. In our scenario, the pursuer enters the safety area of the evader headed for collision, while the latter executes a fast evasive motion. Control schemes are designed for both the pursuer and the evader. They are structurally identical, although the objectives are different: the pursuer tries to align its direction of motion with the line-of-sight to the evader, whereas the evader tries to move in a direction orthogonal to the line-of-sight to the pursuer. At the core of the control scheme is a maneuver planning module which makes use of closed-form expressions exclusively. This allows its use in a replanning framework, where each robot updates its motion plan upon completion of a step to account for the perceived motion of the other. Simulation and experimental results on NAO humanoids reveal an interesting asymptotic behavior which was predicted using unicycle as template models for trajectory generation