This paper addresses the problem of planning the motion of a mobile robot with a limited sensory field-of-view in an unknown dynamic environment. In such a situation, the upper-bounded planning time prevents from computing a complete motion to the goal, partial motion planning is in order. Besides the presence of moving obstacles whose future behaviour is unknown precludes absolute motion safety (in the sense that no collision will ever take place whatever happens) is impossible to guarantee. The stance taken herein is to settle for a weaker level of motion safety called passive motion safety: it guarantees that, if a collision takes place, the robot will be at rest. The primary contribution of this paper is PassPMP, a partial motion planner enforcing passive motion safety. PassPMP periodically computes a passively safe partial trajectory designed to drive the robot towards its goal state. Passive motion safety is handled using a variant of the Inevitable Collision State (ICS) concept called Braking ICS, i.e. states such that, whatever the future braking trajectory of the robot, a collision occurs before it is at rest. Simulation results demonstrate how PassPMP operates and handles limited sensory field-of-views, occlusions and moving obstacles with unknown future behaviour. More importantly, PassPMP is provably passively safe.

This paper addresses the problem of navigating a mobile robot with a limited field-of-view in a unknown dynamic environment. In such a situation, absolute motion safety, i.e. such that no collision will ever take place whatever happens, is impossible to guarantee. It is therefore settled for a weaker level of motion safety dubbed passive motion safety: it guarantees that, if a collision takes place, the robot will be at rest. Passive motion safety is tackled using a variant of the Inevitable Collision State (ICS) concept called Braking ICS, i.e. states such that, whatever the future braking trajectory of the robot, a collision occurs before it is at rest. Passive motion safety is readily obtained by avoiding Braking ICS at all times. Building upon an existing Braking ICS-Checker, i.e. an algorithm that checks if a given state is a Braking ICS or not, this paper presents a reactive collision avoidance scheme called PASSAVOID. The main contribution of this paper is the formal proof of PASSAVOID's passive motion safety. Experiments in simulation demonstrates how PASSAVOID operates.

This paper addresses the problem of provably safe navigation for a mobile robot with a limited field-of-view placed in a unknown dynamic environment. In such a situation, absolute motion safety (in the sense that no collision will ever take place whatever happens in the environment) is impossible to guarantee in general. It is therefore settled for a weaker level of motion safety dubbed passive motion safety: it guarantees that, if a collision is inevitable, the robot will be at rest. The primary contribution of this paper is a relaxation of the Inevitable Collision State (ICS) concept called Braking ICS. A Braking ICS is a state for which, no matter what the future trajectory of the robot is, it is impossible to stop before a collision takes place. Braking ICS are designed with a passive motion safety perspective for robots with a limited field-of-view in unknown dynamic environments. Braking ICS are formally defined and a number of important properties are established. These properties are then used to design a Braking ICS checker, i.e. an algorithm that checks whether a given state is a Braking ICS or not. In a companion paper, it is shown how the Braking ICS checker can be integrated into a reactive navigation scheme whose passive motion safety is provably guaranteed.

The execution performances of the Sweeney, Robertson, Tocher (SRT) division algorithm depend on two parameters: the radix-r and the redundancy factor p. In this paper, a study of the effect of these parameters on the division performances is presented. At each iteration, the SRT algorithm performs a multiplication by the quotient digit qi+1. This last can be just a simple shift, if the digit qii+1is a power of two (qi+1= 2k), otherwise, the SRT iteration needs a multiplier. We propose, in this work, an approach to circumvent this multiplication by decomposing the quotient digit qi+1into two or three terms multiples of 2. Then, the multiplication is carried out by simple shifts and a carry save addition. The implementation of this approach on Virtex-II field-programmable gate-array (FPGA) circuits gives best performances than the approach which uses the embedded multipliers 18times18 bits. The iterations delays are operands sizes independent. The reduction tree delays are at most equivalent to the delay of two Virtex-II slices. This approach was tested for the 4, 8, and 16 radixes in the two cases of minimum and maximum redundancy factors. By this study, we conclude that the use of the radix-8 with a maximum redundancy factor gives the best performances by using our approach for the double precision computation of the SRT division.