Prajwal Thakur*^{1 }
M. Nomaan Qureshi*^{1 }
Arun Kumar Singh^{2 }
Y V S Harish^{1 }
Pushkal Katara^{1 }
Houman Masnavi^{2 }
K. Madhava Krishna^{1 }
Brojeshwar Bhowmick^{3 }

^{1} IIIT Hyderabad, India
^{2} Institute of Technology, University of Tartu
^{3} TCS Research, Kolkata, India

This paper presents a real-time algorithm for computing the optimal sequence and motion plans for a fixedbase manipulator to pick and place a set of given objects. The optimality is defined in terms of the total execution time of the sequence or its proxy, the arc-length in the joint-space. The fundamental complexity stems from the fact that the optimality metric depends on the joint motion, but the task specification is in the end-effector space. Moreover, mapping between a pair of end-effector positions to the shortest arclength joint trajectory is not analytic; instead, it entails solving a complex trajectory optimization problem. Existing works ignore this complex mapping and use the Euclidean distance in the end-effector space to compute the sequence. In this paper, we overcome the reliance on the Euclidean distance heuristic by introducing a novel data-driven technique to estimate the optimal arc-length cost in joint space (a.k.a the value function) between two given end-effector positions. We parametrize the value function as a Neural Network and motivate a niche choice for its architecture, inspired by the works on metric learning. The learned value function is then used as an edge cost in a capacitated vehicle routing problem (CVRP) setup to compute the optimal visitation sequence. Finally, we optimize over the input space of the learnt value function network to propose a novel Inverse Kinematics (IK) algorithm that produces substantially shorter joint arc-length trajectories than existing approaches while executing the computed optimal sequence. We show that our sequence planner, in combination with our proposed IK, offers a substantial improvement in joint arc-length over existing state-of-the-art while maintaining scalability to a large number of objects.