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Robotic systems are routinely used in the logistics industry to enhance operational efficiency, but the design of robot workspaces remains a complex and manual task, which limits the system's flexibility to changing demands. This paper aims…

We present a method for establishing invariant manifolds for saddle--center fixed points. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs, and does not require rigorous…

Transverse linearization-based approaches have become among the most prominent methods for orbitally stabilizing feedback design in regards to (periodic) motions of underactuated mechanical systems. Yet, in an $n$-dimensional state-space,…

Achieving quantum-limited motional control of optically trapped particles beyond the sub-micrometer scale is an outstanding problem in levitated optomechanics. A key obstacle is solving the light scattering problem and identifying particle…

We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…

Simplified models are useful to increase the computational efficiency of a motion planning algorithm, but their lack of accuracy have to be managed. We propose two feasibility constraints to be included in a Single Rigid Body Dynamicsbased…

We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques,…

We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…

We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…

To overcome the obstructions imposed by high-dimensional bipedal models, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The process begins with trajectory optimization to design an…

Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…

Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…

The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…

Symbolic motion planning for robots is the process of specifying and planning robot tasks in a discrete space, then carrying them out in a continuous space in a manner that preserves the discrete-level task specifications. Despite progress…

A small variation of the circular shape of the hodograph theorem states that for every elliptical solution of the two-body problem, it is possible to find an appropriate inertial frame such that the speed of the bodies is constant. We use…

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…

The three body problem is a special case of the n body problem where one takes the initial positions and velocities of three point masses and attempts to predict their motion over time according to Newtonian laws of motion and universal…

The general problem of planning feasible trajectories for multimodal robots is still an open challenge. This paper presents a whole-body trajectory optimisation approach that addresses this challenge by combining methods and tools developed…

This paper introduces a methodology for task-specific design optimization of multirotor Micro Aerial Vehicles. By leveraging reinforcement learning, Bayesian optimization, and covariance matrix adaptation evolution strategy, we optimize…