Publications

Conference papers

[C-1] "Gait Generation using Intrinsically Stable MPC in the Presence of Persistent Disturbances", Filippo M. Smaldone, Nicola Scianca, Valerio Modugno, Leonardo Lanari, Giuseppe Oriolo, 2019 IEEE-RAS International Conference on Humanoid Robots, (pdf, video).

Abstract:

From a control point of view, humanoid gait generation can be seen as a problem of tracking a suitable ZMP trajectory while guaranteeing internal stability. In the presence of disturbances, both these aspects are at risk, and a fall may ultimately occur. In this paper, we extend our previously proposed Intrinsically Stable MPC (IS-MPC) method, which guarantees stable tracking for the unperturbed case, to the case of persistent disturbances. This is achieved by designing a disturbance observer whose estimate is used to set up a modified stability constraint for the QP problem. The method is validated by MATLAB tests as well as dynamic simulations for a NAO humanoid in DART.

[C-2] "ZMP Constraint Restriction for Robust Gait Generation in Humanoids", Filippo M. Smaldone, Nicola Scianca, Valerio Modugno, Leonardo Lanari, Giuseppe Oriolo, 2020 IEEE-RAS International Conference on Robotics and Automation, (pdf, video).

Abstract:

We present an extension of our previously pro-posed 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 tobe 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.

[C-3] "Robust MPC-Based Gait Generation in Humanoids", Filippo M. Smaldone, Nicola Scianca, Leonardo Lanari, Giuseppe Oriolo, 2020 I-RIM 3D, (pdf , video presentation in italian).

Abstract:

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.

[C-4] "MPC-Based Gait Generation for Humanoids: from Walking to Running", Filippo M. Smaldone, Nicola Scianca, Leonardo Lanari, Giuseppe Oriolo, 2021 I-RIM 3D, (pdf, video presentation).

Abstract:

We present a Model Predictive Control (MPC) algorithm for 3D walking and running in humanoids. The scheme makes use of the Variable Height Inverted Pendulum (VH-IP) as prediction model, and generates a Center of Mass (CoM) trajectory and footstep positions online. The MPC works with the nonlinear dynamics by decomposing the problem into a vertical and a horizontal component. The vertical is solved first making the horizontal dynamics linear time-varying and therefore solvable in real-time. A stability constraint is incorporated to ensure internal stability. The algorithm is validated with dynamic simulations in DART.

[C-5] "Task-Oriented Generation of Stable Motions for Wheeled Inverted Pendulum Robots", Marco Kanneworff, Tommaso Belvedere, Nicola Scianca, Filippo M. Smaldone, Leonardo Lanari, Giuseppe Oriolo, 2022 IEEE-RAS International Conference on Robotics and Automation, (pdf, video).

Abstract:

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.

[C-6] "Handling Non-Convex Kinematic Constraints in MPC-Based Humanoid Gait Generation", Andrew S. Habib, Filippo M. Smaldone, Nicola Scianca, Leonardo Lanari, Giuseppe Oriolo, 2022 IEEE-RSJ International Conference on Intelligent Robots and Systems (pdf, video).

Abstract:

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.

Journal papers

[J-1] "Feasibility-Driven Step Timing Adaptation for Robust MPC-Based Gait Generation in Humanoids", Filippo M. Smaldone, Nicola Scianca, Leonardo Lanari, Giuseppe Oriolo, 2021 IEEE Robotics and Automation Letters with ICRA 2021 presentation, (pdf, video).

Abstract:

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.

[J-2] "From Walking to Running: 3D Humanoid Gait Generation via MPC", Filippo M. Smaldone, Nicola Scianca, Leonardo Lanari, Giuseppe Oriolo, 2022, Frontiers in Robotics and AI (link).

Abstract:

We present a real-time algorithm for humanoid 3D walking and/or running based on a Model Predictive Control (MPC) approach. The objective is to generate a stable gait that replicates as closely as possible a footstep plan, i.e., a sequence of candidate footstep positions and orientations with associated timings. For each footstep, the plan also specifies an associated reference height for the Center of Mass (CoM) and whether the robot should reach the footstep by walking or running. The scheme makes use of the Variable-Height Inverted Pendulum (VH-IP) as prediction model, generating in real-time both a CoM trajectory and adapted footsteps. The VH-IP model relates the position of the CoM to that of the Zero Moment Point (ZMP); to avoid falling, the ZMP must be inside a properly defined support region (a 3D extension of the 2D support polygon) whenever the robot is in contact with the ground. The nonlinearity of the VH-IP is handled by splitting the gait generation in two consecutive stages, both requiring to solve a quadratic program. Thanks to a particular triangular structure of the VH-IP dynamics, the first stage deals with the vertical dynamics using the Ground Reaction Force (GRF) as decision variable. Using the prediction given by the first stage, the horizontal dynamics becomes linear time-varying. During flight phases the VH-IP collapses to a free-falling mass model. The proposed formulation incorporates constraints in order to maintain physically meaningful values of the GRF, keep the ZMP in the support region during contact phases, and ensure that the adapted footsteps are kinematically realizable. Most importantly, a stability constraint is enforced on the time-varying horizontal dynamics to guarantee a bounded evolution of the CoM with respect to the ZMP. Furthermore, we show how to extend the technique in order to perform running on tilted surfaces. We also describe a simple technique that receives in input high-level velocity commands and generates a footstep plan in the form required by the proposed MPC scheme. The algorithm is validated via dynamic simulations on the full-scale humanoid robot HRP-4, as well as experiments on the small-sized robot OP3.