Adaptive task planning is fundamental to ensuring effective and seamless human–robot collaboration. This article introduces a robot task planning framework that takes into account both human leading/following preferences and performance, specifically focusing on task allocation and scheduling in collaborative settings. We present a proactive task allocation approach with three primary objectives: 1) enhancing team performance; 2) incorporating human preferences; and 3) upholding a positive human perception of the robot and the collaborative experience. Through a user study, involving an autonomous mobile manipulator robot working alongside participants in a collaborative scenario, we confirm that the task planning framework successfully attains all three intended goals, thereby contributing to the advancement of adaptive task planning in human–robot collaboration. This article mainly focuses on the first two objectives, and we discuss the third objective, participants’ perception of the robot, tasks, and collaboration in a companion article.