Nicolas Petit

The paper considers the problem of controlling the shape of the moving interface between two fluids contained in a during its filling. This system is subject to . The interface shape dynamics is described using a modal decomposition where each mode is governed by a non-smooth ordinary differential equation with a random initial condition that is initially unknown. Once the interface is visibly non circular, a motion planning technique is employed to control the growth of the modes with the goal of approaching a shape of interest. The paper describes the dynamics at stake, studies its reachability property and proposes a constructive method to solve the motion planning problem. Some numerical experiments illustrate the presented methodology.

The paper addresses the rehabilitation of disabled patients using a lower-limb fully-actuated exoskeleton. We propose a novel numerical method to replan the current step without jeopardizing stability. Stability is evaluated in the light of a simple linear time-invariant surrogate model. The method’s core is the analysis of an input-constrained optimal control problem with state specified at an unspecified terminal time. A detailed study of the extremals given by Pontryagin Maximum Principle is sufficient to characterize its feasibility. This allows a fast replanning strategy. The efficiency of the numerical algorithm (resolution time below 1 ms) yields responsiveness to the patient’s request. Realistic simulations on a full-body model of the patient-exoskeleton system stress that cases of practical interest for physiotherapists are well-addressed.

The paper addresses the rehabilitation of disabled patients using a lower-limb fully-actuated exoskeleton. We propose a novel numerical method to replan the current step without jeopardizing stability. Stability is evaluated in the light of a simple linear time-invariant surrogate model. The method's core is the analysis of an input-constrained optimal control problem with state specified at an unspecified terminal time. A detailed study of the extremals given by Pontryagin Maximum Principle is sufficient to characterize its feasibility. This allows a fast replanning strategy. The efficiency of the numerical algorithm (resolution time below 1 ms) yields responsiveness to the patient's request. Realistic simulations on a full-body model of the patient-exoskeleton system stress that cases of practical interest for physiotherapists are well-addressed.

This paper presents a novel observer for estimating the state of a legged robot with deformations in the structure, taking into account the dynamic nature of walking motions. Specifically, it considers a robot with several punctual deformations, whose rotations are estimated using low-cost IMUs. To compensate for the linear acceleration corrupting the measurement of gravity in the accelerometer, this observer exploits the robot's kinematics model. Namely, it combines gyroscope and accelerometer signals, encoder measurements, and attitude estimates from the previous IMUs to reconstruct the linear velocity of a given IMU. This reconstructed measurement is used to estimate the tilt (roll and pitch) of the current IMU, which is then exploited to propagate the linear velocity to the next sensor. The resulting cascade of observers, called MOVIE, is experimentally benchmarked on the exoskeleton Atalante, where it outperforms our previous observer, relying on a quasi-static assumption. This observer is then used in closed-loop control, to compensate for the effect of deformations while walking, resulting in an improved walk.

This paper studies the problem of vertical powered landing through a non-negligible density atmosphere. Several constraints are considered, one of them prevents hovering flight. The findings of the paper extend the results from the literature on atmosphere-free problems. The main contribution establishes the nature of the fuel-optimal control sequence. Sufficient and necessary conditions are provided that guarantee the Min-Max nature of the normal extremals. Abnormal extremals are also shown to be either Min or Max.