Handheld virtual reality (VR) controllers are necessary for creating immersive experiences. In this paper, we propose a gated RNN-based sequence model that estimates the joint torques of a serially linked handheld VR system interface from a sequential position input. In our previous study, we proposed a motion planning algorithm for articulated systems based on the active contour model that optimizes the positions of each joint torque based on the measured base position (6-Degrees of Freedom). Because the position-to-position scheme, which calculates the joint positions from a given base position, illustrated several limitations concerning safety (i.e. unable to handle unexpected contact with the surroundings), our current study proposes a position-to-torque generation scheme that estimates the joint torques from the measured base position sequences. To that end, we trained the sequences of joint torques and the sequence of the 6-DoF base position as a supervised learning task. To model the multivariate temporal information of the sequences, we employed a gated recurrent unit. The experimental results validate the successful generation of joint trajectory profiles.