Point Cloud based Dynamical System Modulation for Reactive Avoidance of Convex and Concave Obstacles Matteo Saveriano and Dongheui Lee Abstract— The ability of the robot to avoid undesired colli- sions with humans and objects in its workspace is of importance in the field of human-robot interaction. In this paper, we propose an algorithm which allows the robot to avoid obstacles and to reach the assigned goal as long as the goal does not lie within obstacles. For this purpose, dynamical system modulation approach is adopted which ensures the avoidance of convex and concave obstacles. A modulation matrix can be calculated directly from the point cloud data of obstacles in the scene, without the need of analytical representation of the obstacles. This matrix modulates a generic first order dynamical system, used to generate the goal. In this way we guarantee the obstacles avoidance and the reaching of the goal. The effectiveness of the proposed approach is validated with numerical simulations and experiments on a 7 DOF KUKA light weight arm. I. I NTRODUCTION When a human and a robot are in a close cooperation, the robot is required to adapt quickly to various situations and to eventual external disturbances ensuring the operator safety. A quick adaptation means that the robot has to react to several kind of external perturbations in real-time. Examples of these external disturbances are: changes in the goal position to reach, presence of unknown obstacles, accidental contacts with the human or with other objects. A feasible solution for reacting in real-time to the external perturbations consists in representing the task as a dynamical system (DS). A DS is robust against perturbations, and it ensures the convergence to the goal [1][2]. In order to react to the presence of unknown obstacles and humans, the robot has to modify its motion quickly to avoid collisions. After the avoidance, it is desirable that the robot fulfills the assigned task as long as possible. The methods for generating collisions free paths can be divided into two categories: path planning approach and reactive motion generation approach. The former is complex global approach which is able to find the shortest collision free path even in very complex scenarios with multi degree- of-freedom robots [3]. Despite the possibility to parallelise the algorithms in order to reduce the computation time [4], at present the computation time is still too large to apply this algorithm on-line. The latter includes local algorithms which change the robot path in real-time. A widely used approach is based on an artificial potential field [5]. The idea is to assign an attractive force to the goal and to shape the obstacles as Authors are with Fakult¨ at f¨ ur Elektrotechnik und Informa- tionstechnik, Technische Universit¨ at M¨ unchen, Munich, Germany matteo.saveriano@tum.de, dhlee@tum.de. Fig. 1. The KUKA Light-Weight-Robot IV+ goes in and out of a box avoiding collisions. This task is useful, for example, to ask the robot to take something in the box. repulsive forces, so as to reach the target avoiding obstacles. The potential field technique is applied in [6], where an algorithm to extract information about the location of the obstacles directly from the image plane of an RGB-D sensor is proposed. One drawback of the potential field approach is that the motion can stop in a local minimum even if a collision-free path to the goal exists. A solution to skip the local minima is proposed in [7] by combining the benefits of the path planning algorithms with the velocity of the reactive techniques. In this method, the initial elastic band is computed off-line using a path planning algorithm, which results in a collision free path. In the presence of obstacle, the band is deformed by applying repulsive forces. However, if the path being executed gets infeasible because of the obstacles coming into its way, the reshaping method cannot be applied any more, and an off- line replanning step is needed [8]. Other researchers propose to avoid local minima by mod- ifying the dynamics of a particular system of differential equations. For example in [9][10] an additive term is ap- plied to a discrete Dynamic Movement Primitive (DMP) [2] in order to deform the trajectory and avoid a point obstacle. The global stability of the modified system is proved with static obstacles using the Lyapunov theorem. In [11] a potential field is applied to a second order system with varying stiffness that generates a smooth collision- free path. A combination of potential fields and circular fields is proposed in [12]. Several experiments show the good convergence properties to the goal of this approach, also in very complex scenarios. The mentioned approaches work only with a specific dynamical system, reducing the