  Offline optimal planning of trajectories for redundant robots along
prescribed task space paths is usually broken down into two consecutive
processes: first, the task space path is inverted to obtain a joint space path,
then, the latter is parametrized with a time law. If the two processes are
separated, they cannot optimize the same objective function, ultimately
providing sub-optimal results. In this paper, a unified approach is presented
where dynamic programming is the underlying optimization technique. Its
flexibility allows accommodating arbitrary constraints and objective functions,
thus providing a generic framework for optimal planning of real systems. To
demonstrate its applicability to a real world scenario, the framework is
instantiated for time-optimality on Franka Emika's Panda robot. The well-known
issues associated with the execution of non-smooth trajectories on a real
controller are partially addressed at planning level, through the enforcement
of constraints, and partially through post-processing of the optimal solution.
The experiments show that the proposed framework is able to effectively exploit
kinematic redundancy to optimize the performance index defined at planning
level and generate feasible trajectories that can be executed on real hardware
with satisfactory results.
