It has been almost two decades since the first globally tracking convergent adaptive controllers were derived for robot with dynamic uncertainties. However, the problem of concurrent adaptation to both kinematic and dynamic uncertainties has never been systematically solved. This is the subject of this paper. We derive a new adaptive Jacobian controller for trajectory tracking of robot with uncertain kinematics and dynamics. It is shown that the robot end effector is able to converge to a desired trajectory with the uncertain kinematics and dynamics parameters being updated online by parameter update laws. The algorithm requires only to measure the end-effector position, besides the robot's joint angles and joint velocities. The proposed controller can also be extended to adaptive visual tracking control with uncertain camera parameters, taking into consideration the uncertainties of the nonlinear robot kinematics and dynamics. Experimental results are presented to illustrate the performance of the proposed controllers. In the experiments, we demonstrate that the robot's shadow can be used to control the robot.

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Abstract-Few comparisons have been performed across torque controllers for exoskeletons, and differences among devices have made interpretation difficult. In this study, we compared the torque-tracking performance of nine control methods, including variations on classical feedback control, modelbased control, adaptive control and iterative learning. Each was tested with four high-level controllers that determined desired torque based on time, joint angle, a neuromuscular model, or electromyography. Controllers were implemented on a tethered ankle exoskeleton with series elastic actuation. Measurements were taken while one human subject walked on a treadmill at 1.25 m·s -1 for one hundred steady-state steps. The combination of proportional derivative control with iterative learning resulted in the lowest errors for all high-level controllers. With timebased desired torque, rms errors were 0.6 N·m (1.3% of peak torque) step by step, and 0.1 N·m (0.2%) on average. These results indicate that model-free, integration-free feedback control is suited to the uncertain dynamics of the human-robot system, while iterative learning is effective in the cyclic task of walking.

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