New robot control algorithms in terms of quasi-velocities

We present new control algorithms for robots whose dynamics are described in terms of quasi-velocities. We incorporate into the forward dynamics algorithms the new control laws in terms of normalized and unnormalized quasi-velocities. We consider two cases: end point trajectory tracking and trajectory tracking algorithms. It is shown that by proper choosing of the Lyapunov function candidate a dynamic system with appropriate feedback is asymptotically and exponentially stable and follows a desired trajectory in the task space. The control laws track the desired position, velocity, and acceleration in Cartesian space. All control laws have new architecture in the sense that they are derived in the so called quasi-velocity and quasi-force space. We also propose a sliding mode control in quasi-velocity and quasi-force spaces.