Related papers: The dog-and-rabbit chase problem
The pursuit-evasion game is studied for two adversarial active agents, modelled as a deterministic self-steering pursuer and a stochastic, cognitive evader. The pursuer chases the evader by reorienting its propulsion direction with limited…
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the…
Animals and robots exist in a physical world and must coordinate their bodies to achieve behavioral objectives. With recent developments in deep reinforcement learning, it is now possible for scientists and engineers to obtain sensorimotor…
We present a deep reinforcement learning (deep RL) algorithm that consists of learning-based motion planning and imitation to tackle challenging control problems. Deep RL has been an effective tool for solving many high-dimensional…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the…
Teaching Robotics is about empowering students to create and configure robotics devices and program computers to nurture in students the skill sets necessary to play an active role in society. The robot in Figure 1 focuses on the design of…
This is a follow-up tutorial article of our previous article entitled "Robot Basics: Representation, Rotation and Velocity". For better understanding of the topics covered in this articles, we recommend the readers to first read our…
Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to…
Diagram chasing is a customary proof method used in category theory and homological algebra. It involves an element-theoretic approach to show that certain properties hold for a commutative diagram. When dealing with abelian categories for…
We present three new diagnostic prediction problems inspired by classical-conditioning experiments to facilitate research in online prediction learning. Experiments in classical conditioning show that animals such as rabbits, pigeons, and…
Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
The classical model that describes the motion of an atom in a magnetic trap is solved in order to investigate the relationship between the failure of the usual adiabatic approximation assumption and the physical parameters of the trap. This…
Real-time computation of optimal control is a challenging problem and, to solve this difficulty, many frameworks proposed to use learning techniques to learn (possibly sub-optimal) controllers and enable their usage in an online fashion.…
Animals can learn efficiently from a single experience and change their future behavior in response. However, in other instances, animals learn very slowly, requiring thousands of experiences. Here I survey tasks involving fast and slow…
The problem of reinforcement learning is considered where the environment or the model undergoes a change. An algorithm is proposed that an agent can apply in such a problem to achieve the optimal long-time discounted reward. The algorithm…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We…
Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of the underlying physical problem. For…