Continuum manipulators enable minimally-invasive surgery on the beating heart, but the challenges involved in manually controlling the manipulator's tip position and contact force with the tissue result in failed procedures and complications. The objective of this work is to achieve autonomous robotic control of a continuum manipulator's position and force in a beating heart model. We present a model-less hybrid control approach that regulates the tip position/force of manipulators with unknown kinematics/ mechanics, under unknown constraints along the manipulator's body. The algorithms estimate the Jacobian in the presence of heartbeat disturbances and sensor noise in real time, enabling closed-loop control. Using this model-less control approach, a robotic catheter autonomously traced clinically relevant paths on a simulated beating heart environment while regulating contact force. A gating procedure is used to tighten the treatment margins and improve precision. Experimental results demonstrate the capabilities of the robot (1:4 AE 1:1 mm-1:9 AE 1:4 mm tracking error) while user demonstrations show the difficulty of manually performing the same task (2:6 AE 2:0 mm-4:3 AE 3:9 mm tracking error). This new, robotically-enabled contiguous ablation method could reduce ablation path discontinuities, improve consistency of treatment, and therefore improve clinical outcomes.