Josep Martí-Saumell

Josep Martí-Saumell, Joan Solà, Angel Santamaria-Navarro et al.

Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.

Carlos Mastalli, Wolfgang Merkt, Josep Marti-Saumell et al.

Differential dynamic programming (DDP) is a direct single shooting method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit roll-out/integration of the system dynamics. However, it suffers from numerical instability and, when compared to direct multiple shooting methods, it has limited initialization options (allows initialization of controls, but not of states) and lacks proper handling of control constraints. In this work, we tackle these issues with a feasibility-driven approach that regulates the dynamic feasibility during the numerical optimization and ensures control limits. Our feasibility search emulates the numerical resolution of a direct multiple shooting problem with only dynamics constraints. We show that our approach (named BOX-FDDP) has better numerical convergence than BOX-DDP+ (a single shooting method), and that its convergence rate and runtime performance are competitive with state-of-the-art direct transcription formulations solved using the interior point and active set algorithms available in KNITRO. We further show that BOX-FDDP decreases the dynamic feasibility error monotonically--as in state-of-the-art nonlinear programming algorithms. We demonstrate the benefits of our approach by generating complex and athletic motions for quadruped and humanoid robots. Finally, we highlight that BOX-FDDP is suitable for model predictive control in legged robots.

Josep Marti-Saumell, Angel Santamaria-Navarro, Carlos Ocampo-Martinez et al.

Today's complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the stability problem of a hierarchical losed-loop inverse kinematics algorithm for such highly redundant robots. We present a method to guarantee system stability by performing an online tuning of the closedloop control gains. We define a semi-definite programming problem (SDP) with these gains as decision variables and a discrete-time Lyapunov stability condition as a linear matrix inequality, constraining the SDP optimization problem and guaranteeing the stability of the prioritized tasks. To the best of authors' knowledge, this work represents the first mathematical development of an SDP formulation that introduces stability conditions for a multi-objective closed-loop inverse kinematic problem for highly redundant robots. The validity of the proposed approach is demonstrated through simulation case studies, including didactic examples and a Matlab toolbox for the benefit of the community.