Robotic rehabilitation of the upper limb following neurological injury is most successful when subjects are engaged in the rehabilitation protocol. Developing assistive control strategies that maximize subject participation is accordingly an active area of research, with aims to promote neural plasticity and, in turn, increase the potential for recovery of motor coordination. Unfortunately, state-of-the-art control strategies either ignore more complex subject capabilities or assume underlying patterns govern subject behavior and may therefore intervene suboptimally. In this paper, we present a minimal assist-as-needed (mAAN) controller for upper limb rehabilitation robots. The controller employs sensorless force estimation to dynamically determine subject inputs without any underlying assumptions as to the nature of subject capabilities and computes a corresponding assistance torque with adjustable ultimate bounds on position error. Our adaptive input estimation scheme is shown to yield fast, stable, and accurate measurements regardless of subject interaction and exceeds the performance of current approaches that estimate only position-dependent force inputs from the user. Two additional algorithms are introduced in this paper to further promote active participation of subjects with varying degrees of impairment. First, a bound modification algorithm is described, which alters allowable error. Second, a decayed disturbance rejection algorithm is presented, which encourages subjects who are capable of leading the reference trajectory. The mAAN controller and accompanying algorithms are demonstrated experimentally with healthy subjects in the RiceWrist-S exoskeleton.