Related papers: Discrete Mechanics and Optimal Control for Passive…
Robust and energy-efficient bipedal locomotion in robotics is still a challenging topic. In order to address issues in this field, we can take inspiration from nature, by studying human locomotion. The Spring-Loaded Inverted Pendulum (SLIP)…
Some problems on variations are raised for classical discrete mechanics and field theory and the difference variational approach with variable step-length is proposed motivated by Lee's approach to discrete mechanics and the difference…
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than…
We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is…
This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the…
In this study, we present a simulation-based numerical method for solving a class of singularly perturbed second-order differential equations that come from a simplified biologically motivated model of human gait. Important physical factors…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
We introduce generalized Galerkin variational integrators, which are a natural generalization of discrete variational mechanics, whereby the discrete action, as opposed to the discrete Lagrangian, is the fundamental object. This is achieved…
In this paper, we will report our efforts in designing closed-loop feedback for the thruster-assisted walking of bipedal robots. We will assume for well-tuned supervisory controllers and will focus on fine-tuning the joints desired…
There are different physics-based approaches for analysing pedestrian movement. Physics-based methods like statistical mechanics-based models apply the laws of physics to drive equations for analysing crowd behaviour. This paper will…
We present a highly reactive controller which enables bipedal robots to blindly walk over various kinds of uneven terrains while resisting pushes. The high level motion planner does fast online optimization for footstep locations and Center…
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a…
In this work, we introduce a control framework that combines model-based footstep planning with Reinforcement Learning (RL), leveraging desired footstep patterns derived from the Linear Inverted Pendulum (LIP) dynamics. Utilizing the LIP…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
Sprawling locomotion in vertebrates, particularly salamanders, demonstrates how body undulation and spinal mobility enhance stability, maneuverability, and adaptability across complex terrains. While prior work has separately explored…
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties…
A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the…
In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows…
We develop the theory of discrete time Lagrangian mechanics on Lie groups, originated in the work of Veselov and Moser, and the theory of Lagrangian reduction in the discrete time setting. The results thus obtained are applied to the…