Dynamical System based Robotic Motion Generation with Obstacle Avoidance
The problem of real time motion generation to a target with obstacle avoidance is considered. A second order dynamical system having the target as a unique globally asymptotically stable equilibrium is modified in the presence of obstacles by an additive signal whose design is based on the Prescribed Performance Control methodology. It is proved that obstacle avoidance and dynamical system stability is guaranteed and that the target remains asymptotically stable. Simulations are utilized to reveal the cases where the proposed scheme outperforms the modulated dynamical system and the constrained optimization priority framework. Experimental results further validate the theoretical findings.
In a multiple task priority framework generalized for inequality tasks , obstacle avoidance is expressed as one sided inequality constraints on the robot’s velocities. In this framework a constrained minimization of a quadratic function under equality and inequality constraints is formulated and solved by a general purpose optimization algorithm (HQP). The solution does not avoid local minima. Moreover, the computational cost of such generalized solution is high despite improvements of the solver reported in . The elementary form of constraints like the joint limits and obstacles calls for their explicit consideration which could lead to computationally more efficient algorithms, for example and in the case of joint limits, the works of , .
In this work, an additive term is utilized for the purpose of obstacle avoidance with a second order dynamical system having the target as a unique stable equilibrium as in . In contrast to  however, an obstacle is assumed to be contained in a convex region defined by a generalized ellipsoid. Moreover, the obstacle avoidance signal is designed following the prescribed performance control methodology (PPC) introduced in . PPC has been applied in the design of robot position controllers ,  and as it allows the designer to impose bounds on the output signals of nonlinear systems has already been successfully utilized to impose spatial and joint limit constraints, , . In this work, it is proved using Lyapunov’s theory that obstacle avoidance and modified system stability is guaranteed and that the target remains asymptotically convergent. It is illustrated in simulation for non-convex scene cases in which it outperforms the method of dynamical system modulation (MDS) of  and HQP . Experimental results utilizing a KUKA LWR4+ are also provided to illustrate the method’s performance.
In this paper we propose an obstacle avoidance signal designed according to the prescribed performance control methodology, which affects the motion generated by a second order dynamical system having the target as a unique stable equilibrium. The proposed scheme, utilizing generalized ellipsoids for the obstacles, is proved to guarantee collision avoidance and system stability retaining the asymptotic stability of the target. It is shown in simulations to avoid traps in non convex scenes as opposed to dynamical system modulation and priority level constraint optimization techniques. Experimental results with KUKA LWR4+ demonstrate its smooth effective performance in an environment involving a variety of obstacles.
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