Obstacle avoidance planning for redundant manipulator based on variational method

Abstract

Original scientific paper To reduce the excessive joints movement, this paper proposed a new obstacle avoidance method for a redundant manipulator. In this method, we designed the performance evaluation functional to realize the shortest joints motion path of manipulator, and deduced the gradient vector optimizing index by variational method to make the joint movement minimum during obstacle avoiding. Meanwhile, in order to avoid the obstacle avoidance algorithm failure or joints exceeding their limits, which arose from the great difference between least-norm solution and homogeneous solution of velocity inverse kinematics of the manipulator, this paper used 2-norm continuous function to adjust homogeneous solution factor of gradient projection method dynamically. To verify the validity of the proposed obstacle avoidance method in the paper, simulation experiments were conducted on a 7-DOF redundant manipulator. The results show that, compared to the traditional gradient projection method for obstacle avoidance, the proposed algorithm in this paper has decreased the displacement of joint 1 to joint 6 by 38,3 %, 83,3 %, 3,81 %, 7,85 %, 50,1 % and 45,6 % respectively, and the total displacement of prismatic joints and revolute joints has reduced 62,2 % and 26,4 %. At the same time, the changes of joint 1 to joint 6's velocity and acceleration between initial time and final time during obstacle avoiding has been decreased 43,2 %, 97,3 %, 2,23 %, 36,6 %, 96,7 %, 72,7 % (velocity) and 91,04 %, 98,28 %, 73,33 %, 98,40 %, 93,86 % and 91,94 % (acceleration) respectively. The test validated that the proposed obstacle avoidance method based on variational method is feasible and practicable. Keywords: gradient projection; obstacle avoidance; path planning; variational method; redundant manipulator Planiranje izbjegavanja prepreka kod redundantnog manipulatora na temelju varijacijske metodeIzvorni znanstveni članak U svrhu smanjenja prekomjernog pomicanja zglobova, u radu se predlaže nova metoda za izbjegavanje prepreka kod redundantnog manipulatora. U toj smo metodi dizajnirali funkcionalnu procjenu pokreta kako bismo dobili najkraću stazu kretanja zgloba manipulatora i dobili indeks optimizacije vektora gradijenta primjenom varijacijske (variational) metode da bi za vrijeme izbjegavanja prepreke kretanje zgloba bilo minimalno. U međuvremenu, kako bismo izbjegli neuspjeh algoritma za izbjegavanje prepreke ili prekoraćenje krajnjih granica zglobova, do kojih je došlo zbog velike razlike između solucije najmanje norme i homogene solucije kinematike inverzne brzine manipulatora, u radu je primijenjena kontinuirana funkcija 2-norme da bi se dinamički podesio homogeni faktor rješenja metode projekcije gradijenta. Da bi se provjerila ispravnosti u radu predložene metode izbjegavanja prepreka, provedeni su simulacijski eksperimenti na 7-DOF redundantnom manipulatoru. Rezultati pokazuju da u usporedbi s tradicionalnom metodom projekcije gradijenta za izbjegavanje prepreka, u radu predloženim algoritmom smanjio se pomak zgloba 1 d...