Related papers: Using the Geometric Phase to Optimise Planar Somer…
Isolated mechanical systems -- e.g., those floating in space, in free-fall, or on a frictionless surface -- are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers…
Elongate animals and robots use undulatory body waves to locomote through diverse environments. Geometric mechanics provides a framework to model and optimize such systems in highly damped environments, connecting a prescribed shape change…
We propose a new method for shape recognition and retrieval based on dynamic programming. Our approach uses the dynamic programming algorithm to compute the optimal score and to find the optimal alignment between two strings. First, each…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
In this paper, we consider the sequential decision problem where the goal is to minimize the general dynamic regret on a complete Riemannian manifold. The task of offline optimization on such a domain, also known as a geodesic metric space,…
In this work we propose to combine the advantages of learningbased and combinatorial formalisms for 3D shape matching. While learningbased methods lead to state-of-the-art matching performance, they do not ensure geometric consistency, so…
The complex dynamics of agile robotic legged locomotion requires motion planning to intelligently adjust footstep locations. Often, bipedal footstep and motion planning use mathematically simple models such as the linear inverted pendulum,…
For multi-limbed robots, motion planning with posture and force constraints tends to be a difficult optimization problem due to nonlinearities, which also present extended solve times. We propose a multi-stage optimization framework with…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…
Robots are moving towards applications in less structured environments, but their model-based controllers are challenged by the tasks' complexity and intrinsic environmental unpredictability. Studying biological motor control can provide…
This paper presents an optimal motion planning framework to generate versatile energy-optimal quadrupedal jumping motions automatically (e.g., flips, spin). The jumping motions via the centroidal dynamics are formulated as a 12-dimensional…
The wave description of geometric phase uses the superposition of light waves to explain the geometric phase's origin. While our previous work focused on a basis of linearly polarized waves, here we show that the same concepts can be…
Many robotic systems locomote using gaits - periodic changes of internal shape, whose mechanical interaction with the robot's environment generate characteristic net displacements. Prominent examples with two shape variables are the low…
We study self propelled stokesian robots composed of assemblies of balls, in dimensions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…
Automatically generating agile whole-body motions for legged and humanoid robots remains a fundamental challenge in robotics. While numerous trajectory optimization approaches have been proposed, there is no clear guideline on how the…
Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of…
In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction…
The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same…