We consider kinematic chains evolving on a nite{ dimensional Lie group G under nonholonomic constraints, where snake{like global motion is induced by shape variations of the system. In particular, we consider the case when the evolution of the system is restricted to a subspace h of the corresponding Lie algebra G; where h is not a subalgebra of G and it generates the whole algebra under Lie br...

Many practical dextrous manipulation tasks involve large-scale motion of the grasped object while maintaining a stable grasp. To plan such tasks, one must control both the motion of the object and the contact locations, while also adhering to the workspace constraints typical of multingered hands. In this paper, we integrate the relevant theories of contact kinematics, nonholonomic motion plann...

We present a local approach for planning the motion of a car-like robot navigating among obstacles, suitable for sensor-based implementation. The nonholonomic nature of the robot kinematics is explicitly taken into account. The strategy is to modify the output of a generic local holonomic planner, so as to provide commands that realize the desired motion in a leastsquares sense. A feedback acti...

In this paper we address whole-body manipulation of bulky objects by a humanoid robot. We adopt a “pivoting” manipulation method that allows the humanoid to displace an object without lifting, but by the support of the ground contact. First, the smalltime controllability of pivoting is demonstrated. On its basis, an algorithm for collision-free pivoting motion planning is established taking int...

In this paper, we present a geometric method for motion planning for a fleet of differentially driven mobile robots moving in formation, that explicitly takes in to account their nonholonomic constraints. The relative position of each mobile robot within the formation induces different motion plans for the individual mobile robots. By using a suitable metric, defined on the motions of each mobi...

We present an approach to the problem of mobile robot motion planning in arbitrary cost fields subject to differential constraints. Given a model of vehicle maneuverability, a trajectory generator solves the two point boundary value problem of connecting two points in state space with a feasible motion. We use this capacity to compute a control set which connects any state to its reachable neig...

INTRODUCTION Bevel-tipped flexible needles can be steered in soft tissue to clinical targets along curved paths in 3D while avoiding critical structures. Duty-cycled rotation [1] during insertion allows for control of the curvature of the needle. These capabilities of 3D steerable needles make it potentially suitable for applications such as deep brain stimulation (DBS) and drug delivery to bra...

In this paper, we develop the machinery of exterior diierential forms, more particularly the Goursat normal form for a Pfaaan system, for solving nonholonomic motion planning problems, i.e. planning problems with non-integrable velocity constraints. We apply this technique to solving the problem of steering a mobile robot with n trailers. We present an algorithm for nding a family of transforma...

We present a novel analysis technique to understand the dynamics of a recently described locomotion mode called legless locomotion. Legless locomotion is a locomotion mode available to a legged robot when it becomes high-centered, that is, when its legs do not touch the ground. Under these conditions, the robot may still locomote in the plane by swinging its legs in the air, rocking on its body...