When applying methods of optimal control to motion planning or stabilization problems , some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the underlying optimal control problem. In this article, we provide characterizations for singular trajectories of control-affine systems. We prove that, under gener...

the main objective of this article is to optimize the walking pattern of a 2d humanoid robot with heel-off and toe-off motions in order to minimize the energy consumption and maximize the stability margin. to this end, at first, a gait planning method is introduced based on the ankle and hip joint position trajectories. then, using these trajectories and the inverse kinematics, the position tra...

urban expansion and agriculture intensification are relevant drivers in land degradation (ld)processes in europe due to net loss of land, soil sealing, landscape fragmentation and other negative effects on the environment. this paper explores changes (or “trajectories” of change) in land use and cover (lulc) and their relationship with the consumption of soils in emilia-romagna (northern italy)...

The laws of physics establish the energetic efficiency of our movements. In some cases, like locomotion, the mechanics of the body dominate in determining the energetically optimal course of action. In other tasks, such as manipulation, energetic costs depend critically upon the variable properties of objects in the environment. Can the brain identify and follow energy-optimal motions when thes...

This article considers continuous trajectories of the vector fields induced by two different primal-dual potential-reduction algorithms for solving linear programming problems. For both algorithms, it is shown that the associated continuous trajectories include the central path and the duality gap converges to zero along all these trajectories. For the algorithm of Kojima, Mizuno, and Yoshise, ...

Using mobile sensors to perform optimal measurement and estimation of a distributed parameter system in a domain of interest is considered in this paper. Given parameters, how to optimally plan the motion trajectories of the mobile sensors has been known in the literature, where the purpose of mobile sensing is to best estimate the parameters. Clearly, there is a “chick-and-egg” problem regardi...

Previous work [3, 6, 9, 8, 7, 1] has presented the time optimal trajectories for three classes of non-holonomic mobile robots: steered cars that can only go forwards, steered cars that go forwards or backwards, and differential drives. Each of the vehicles is modelled as a rigid body in the plane with velocity and angular velocity controls. The systems are differentiated only by the bounds on t...

We investigate energy-optimal control of robots with ultracapacitor based regenerative drive systems. Based on a previously introduced framework, a fairly generic model is considered for the robot and the drive system. An optimal control problem is formulated to find point-to point trajectories maximizing the amount of energy regenerated and stored in the capacitor. The optimization problem, it...