Repeatable Motion Planning for Redundant Robots over Cyclic Tasks

We consider the problem of repeatable motion planning for redundant robotic systems performing cyclic tasks in the presence of obstacles. For this open problem, we present a control-based randomized planner, which produces closed collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. The proposed algorithm, which relies on bidirectional search and loop closure in the task-constrained configuration space, is shown to be probabilistically complete. A modified version of the planner is also devised for the case in which configuration-space paths are required to be smooth. Finally, we present planning results in various scenarios involving both free-flying and nonholonomic robots to show the effectiveness of the proposed method

A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

In this paper we propose a new dynamic model, based on quaternions, for tensegrity systems of class-1. Quaternions are used to represent orientations of a rigid body in the 3-dimensional space eliminating the problem of singularities. Moreover, the equations based on quaternions allow to perform more precise calculations and simulations because they do not use trigonometric functions for the representation of angles. We present a thorough introduction of tensegrities and the current state of research. We also introduce the quaternions and provide in the appendix some important details and useful properties. Applying the Euler–Lagrange approach we derive a comprehensive dynamic model, first for a simple rigid bar in the space and, at last, for a class-1 tensegrity system. We present two model forms: a matrix and a vectorial form. The first more compact and easier to write, the latter more suitable to apply the tools and the theory based on vector fields.Postprint (author’s final draft

A comprehensive dynamic model for class-1 tensegrity systems based on quaternions

a b s t r a c t In this paper we propose a new dynamic model, based on quaternions, for tensegrity systems of class-1. Quaternions are used to represent orientations of a rigid body in the 3-dimensional space eliminating the problem of singularities. Moreover, the equations based on quaternions allow to perform more precise calculations and simulations because they do not use trigonometric functions for the representation of angles. We present a thorough introduction of tensegrities and the current state of research. We also introduce the quaternions and provide in the appendix some important details and useful properties. Applying the Euler-Lagrange approach we derive a comprehensive dynamic model, first for a simple rigid bar in the space and, at last, for a class-1 tensegrity system. We present two model forms: a matrix and a vectorial form. The first more compact and easier to write, the latter more suitable to apply the tools and the theory based on vector fields

Enforcing Constraints over Learned Policies via Nonlinear MPC: Application to the Pendubot

In recent years Reinforcement Learning (RL) has achieved remarkable results. Nonetheless RL algorithms prove to be unsuccessful in robotics applications where constraints satisfaction is involved, e.g. for safety. In this work we propose a control algorithm that allows to enforce constraints over a learned control policy. Hence we combine Nonlinear Model Predictive Control (NMPC) with control-state trajectories generated from the learned policy at each time step. We prove the effectiveness of our method on the Pendubot, a challenging underactuated robot

A general framework for task-constrained motion planning with moving obstacles

Consider the practically relevant situation in which a robotic system is assigned a task to be executed in an environment that contains moving obstacles. Generating collision-free motions that allow the robot to execute the task while complying with its control input limitations is a challenging problem, whose solution must be sought in the robot state space extended with time. We describe a general planning framework which can be tailored to robots described by either kinematic or dynamic models. The main component is a control-based scheme for producing configuration space subtrajectories along which the task constraint is continuously satisfied. The geometric motion and time history along each subtrajectory are generated separately in order to guarantee feasibility of the latter and at the same time make the scheme intrinsically more flexible. A randomized algorithm then explores the search space by repeatedly invoking the motion generation scheme and checking the produced subtrajectories for collisions. The proposed framework is shown to provide a probabilistically complete planner both in the kinematic and the dynamic case. Modified versions of the planners based on the exploration–exploitation approach are also devised to improve search efficiency or optimize a performance criterion along the solution. We present results in various scenarios involving non-holonomic mobile robots and fixed-based manipulators to show the performance of the planner

Task-constrained motion planning for underactuated robots

This paper addresses the motion planning problem in the presence of obstacles for underactuated robots that are assigned a geometric task. It is assumed that the robot is subject to kinematic (joint limits, joint velocity bounds) as well as dynamic (torque bounds) constraints. Building on our previous work on task-constrained motion planning, we describe a randomized planner that works directly at the torque level and generates solutions by separating geometric motions from time history. The effectiveness of the proposed approach is shown by planning collision-free swing-up maneuvers for a Pendubot system

An Optimal Mesh Generation for Domains with Koch Type Boundaries

We consider the numerical approximation for a 2D second order parabolic transmission problem across a pre-fractal interface K_n of Koch type; the layer K_n, a polygonal curve, divides a given domain into two non-convex sub-domains \Omega^i_n. The approximation is carried out by a FEM discretization for the space variable and a finite difference scheme in time. The two main difficulties in the approximation and simulations of this type of problems are the generation of a suitable mesh to possibly achieve an optimal rate of convergence and to limit the intrinsic computational cost of numeric approximations. In this talk we will focus on the construction of a mesh compliant with the so-called "Grisvard" conditions which will allow us to obtain an optimal rate of convergence both in space and in time