We propose an effective whole-body MPC controller for locomotion of humanoid robots. Our method generates motions using the full kinematics, allowing it to account for joint limits and to exploit upper-body motions to reject disturbances. Each MPC iteration solves a single QP that considers the interplay between dynamic and kinematic features of the robot. Thanks to our special formulation, we are able to perform a feasibility analysis, which opens the door to future enhancements of functionality and performance, e.g., step adaptation in complex environments. We demonstrate its effectiveness through a campaign of dynamic simulations aimed at highlighting how the joint limits and the use of the angular momentum through upper-body motions are fundamental for maximizing performance, robustness, and ultimately make the robot able to execute more challenging gaits.

We present a whole-body control architecture for the generation of stable task-oriented motions in Wheeled Inverted Pendulum (WIP) robots. Controlling WIP systems is challenging because the successful execution of tasks is subordinate to the ability to maintain balance. Our feedback control approach relies both on partial feedback linearization and Model Predictive Control (MPC). The partial feedback linearization reshapes the system into a convenient form, while the MPC computes inputs to execute the desired task by solving a constrained optimization problem. Input constraints account for actuation limits and a stability constraint is in charge of stabilizing the unstable body pitch angle dynamics. The proposed approach is validated by simulations on an ALTER-EGO robot performing navigation and loco-manipulation tasks.

In most MPC-based schemes used for humanoid gait generation, simple Quadratic Programming (QP) problems are considered for real-time implementation. Since these only allow for convex constraints, the generated gait may be conservative. In this paper we focus on the non-convex reachable region of the swinging foot, also known as Kinematic Admissible Region (KAR), and the corresponding constraint. We represent an approximation of such non-convex region as the union of multiple non-overlapping convex sub-regions. By leveraging the concept of feasibility region, i.e., the subset of the state space for which a QP problem is feasible, and introducing a proper selection criterion, we are able to maintain linearity of the constraints and thus use our Intrinsically Stable Model Predictive Control (IS-MPC) scheme with a negligible additional computational load. This approach allows for a wider range of possible generated motions and is very effective when reacting to a push or avoiding an obstacle, as illustrated in dynamically simulated scenarios.

It is common knowledge that tractor-trailer vehicles are affected by jackknifing, a phenomenon that consists in the divergence of the trailer hitch angle and ultimately causes the vehicle to fold up. For the case of backwards motion, in which jackknifing can also occur at low speeds, we present a control method that drives the vehicle along a reference Cartesian trajectory while avoiding the divergence of the hitch angle. In particular, a feedback control law is obtained by combining two actions: a tracking term, computed using input-output linearization, and a corrective term, generated via IS-MPC, an intrinsically stable MPC scheme which is effective for stable inversion of nonminimum-phase systems. The proposed method has been verified in simulation and experimentally validated on a purposely built prototype.

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.

Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on the capture point. In this paper, we generalize this analysis to the variable-height inverted pendulum (VHIP) and show how it enables 3-D walking over uneven terrains based on capture inputs. Thanks to a tailored optimization scheme, we can compute these inputs fast enough for real-time model predictive control. We implement this approach as open-source software and demonstrate it in dynamic simulations.

In this article, we present an intrinsically stable Model Predictive Control (IS-MPC) framework for humanoid gait generation that incorporates a stability constraint in the formulation. The method uses as prediction model a dynamically extended Linear Inverted Pendulum with Zero Moment Point (ZMP) velocities as control inputs, producing in real time a gait (including footsteps with timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links future ZMP velocities to the current state so as to guarantee that the generated Center of Mass (CoM) trajectory is bounded with respect to the ZMP trajectory. Being the MPC control horizon finite, only part of the future ZMP velocities are decision variables; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several options for the tail are discussed, each corresponding to a specific terminal constraint. A feasibility analysis of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, we prove that recursive feasibility guarantees stability of the CoM/ZMP dynamics. Simulation and experimental results on NAO and HRP-4 are presented to highlight the performance of IS-MPC.

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.

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.

We present a method for performing evasive motions with a humanoid robot. In the considered scenario, the robot is standing in a workspace, when a moving obstacle (e.g., a human, or another robot) enters its safety area and heads towards it; the humanoid must plan and execute in real-time a maneuver that avoids the collision. The proposed method goes through several conceptual steps. Once the entrance of the moving obstacle in the safety area is detected, its approach direction relative to the robot is determined. On the basis of this information, a suitable evasion maneuver represented by footsteps is generated. From these, an appropriate trajectory is computed for the Center of Mass of the humanoid. Finally, joint motion commands are generated so as to track such trajectory. All computations make use of closed-form expressions and are therefore suitable for real-time implementation. The proposed approach is validated via simulations and experiments on a NAO humanoid. The possibility of adapting the basic method so as to be used in a replanning framework is also investigated.

In this paper, we address the problem of planning optimal zero moment point (ZMP) trajectories for the double support phase in bipedal gaits that alternate between single and double support. This is achieved by allowing pre- and post-actuation during the single support phases. Thus, we solve two coupled problems: exact tracking of a given desired ZMP trajectory in the pre- and post-phases (single support), and determination of the desired ZMP during the transition phase (double support). Both are solved while minimizing the overall control energy. We also provide a formal method to assess how the choice of desired ZMP trajectory during the single support phases impacts the overall energy expended during the footstep cycle. Although the obtained solution may not be physically feasible in general, it represents a benchmark to which alternative feasible solutions may be compared. Our approach generalizes previous results that consider only constant output in the pre- and post-phases e.g., allowing pre- and post-phase output from a family of polynomial splines. We evaluate the approach via simulations.

In this paper, we address the problem of gait generation for bipedal robots. We cast the determination of a Center of Mass (CoM) reference trajectory for a given Zero Moment Point (ZMP) desired behaviour as a stable inversion problem for non-minimum phase systems and obtain an analytical solution for any given ZMP trajectory. Our method exploits results from our previous research, in which we derived a family of bounded CoM trajectories associated to a given desired ZMP trajectory.

In this paper we propose a method to perform manual guidance with humanoid robots. Manual guidance is a general model of physical interaction: here we focus on guiding a humanoid by its hands. The proposed technique can be, however, used also for joint object transportation and other tasks implying human-humanoid physical interaction. Using a measure of the Instantaneous Capture Point, we develop an equilibrium-based interaction technique that does not require force/torque or vision sensors. It is, therefore, particularly suitable for low-cost humanoids and toys. The proposed method has been experimentally validated on the small humanoid NAO.

In this paper a tracking controller for rigid robots is presented solving a disturbance attenuation problem with global internal stability in the general case of unknown constant parameters. By using the well-known property of linearity in the parameters for the rigid robot dynamic equations, adaptive and H/sub /spl infin// control are combined successfully. Simulation results show a good behavior of the proposed tracking controller.

The authors investigate the problem of how to achieve a cyclic joint behavior in redundant robots performing cyclic tasks, motivated by the fact that most singularity-free local resolution methods produce nonrepeatable joint motions. A controllability analysis of the inverse kinematic system makes it possible to recover the well-known repeatability conditions of T. Shamir and Y. Yomdin (1988), and to further conclude that no null space velocity can be specified if a repeatable scheme is sought, unless it is chosen as a linear term in the end-effector velocity. The problem of achieving asymptotic cyclicity for a given inversion strategy has been solved via suitable kinematic controls, which guarantee convergence to cyclic joint trajectories along the desired end-effector path. Depending on the structure of the feedforward and feedback terms in the control law, a number of different schemes are proposed, yielding exact or asymptotic end-effector tracking. The stability proofs and the satisfactory simulation results confirm the advantage of using these simple control strategies.>

A general family of asymptotically stabilizing tracking control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems ad the passivity theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through an observability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility.>

The exact eigenfunctions for the slewing link of a robot are found, taking into account a rotating inertia at the base and a payload at the tip. These derive from two equivalent formulations (pseudoclamped and pseudopinned) of the boundary value problem relative to the flexible slewing beam. The exactness of the solution makes it possible to prove the equivalence of these two approaches, which differ in the choice of the noninertial rotating frame. The two related dynamic linear models are then found, and a change of coordinates is given. Experimental measurements validate the theoretical results.>