On the Orientation Planning with Constrained Angular Velocity and Acceleration at Endpoints

This paper presents orientation planning algorithms respecting the requirements of task space trajectory generation, particularly in robotics applications. The proposed algorithms fulfill the following conditions: (i) permitting to impose constraints at angular velocity and acceleration in addition to orientation at endpoints; (ii) rendering continuous acceleration profiles even when interpolating multiple orientations; and (iii) being computationally fast enough for realtime implementation. The generated spline trajectories are essentially a concatenation of polynomial in time curves parameterized by quaternion coefficients. To impose the unitariness condition critically required for quaternion representation of orientation, we develop an on-line update mechanism which successively reparameterizes the polynomials constructing the spline, towards suppressing distortions that the normalization operation might incur. Experiments on an anthropomorphic robot upper-body are carried out to demonstrate the efficacy and real-time compatibility of the proposed algorithms in comparison with a standard spherical interpolation method.