A Dynamic Programming Framework for Optimal Planning of Redundant Robots Along Prescribed Paths With Kineto-Dynamic Constraints

Off-line 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. Compared to numerical solvers, the proposed methodology provides visibility of the underlying resolution process, allowing for further analyses beyond the computation of the optimal trajectory. The effectiveness of the framework is demonstrated on a real 7-degrees-of-freedom serial chain. The issues associated with the execution of optimal trajectories on a real controller are also discussed and addressed. 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.

Time-Optimal Trajectory Planning with Interaction with the Environment

Optimal motion planning along prescribed paths can be solved with several techniques, but most of them do not take into account the wrenches exerted by the end-effector when in contact with the environment. When a dynamic model of the environment is not available, no consolidated methodology exists to consider the effect of the interaction. Regardless of the specific performance index to optimize, this article proposes a strategy to include external wrenches in the optimal planning algorithm, considering the task specifications. This procedure is instantiated for minimum-time trajectories and validated on a real robot performing an interaction task under admittance control. The results prove that the inclusion of end-effector wrenches affect the planned trajectory, in fact modifying the manipulator's dynamic capability.

Discrete fully probabilistic design: a tool to design control policies from examples

We present a discretized design that expounds an algorithm recently introduced in Gagliardi and Russo (2021) to synthesize control policies from examples for constrained, possibly stochastic and nonlinear, systems. The constraints do not need to be fulfilled in the possibly noisy example data, which in turn might be collected from a system that is different from the one under control. For this discretized design, we discuss a number of properties and give a design pipeline. The design, which we term as discrete fully probabilistic design, is benchmarked numerically on an example that involves controlling an inverted pendulum with actuation constraints starting from data collected from a physically different pendulum that does not satisfy the system-specific actuation constraints.

Planning of efficient trajectories in robotized assembly of aerostructures exploiting kinematic redundancy

Aerospace production volumes have increased over time and robotic solutions have been progressively introduced in the aeronautic assembly lines to achieve high-quality standards, high production rates, flexibility and cost reduction. Robotic workcells are sometimes characterized by robots mounted on slides to increase the robot workspace. The slide introduces an additional degree of freedom, making the system kinematically redundant, but this feature is rarely used to enhance performances. The paper proposes a new concept in trajectory planning, that exploits the redundancy to satisfy additional requirements. A dynamic programming technique is adopted, which computes optimized trajectories, minimizing or maximizing the performance indices of interest. The use case is defined on the LABOR (Lean robotized AssemBly and cOntrol of composite aeRostructures) project which adopts two cooperating six-axis robots mounted on linear axes to perform assembly operations on fuselage panels. Considering the needs of this workcell, unnecessary robot movements are minimized to increase safety, the mechanical stiffness is maximized to increase stability during the drilling operations, collisions are avoided, while joint limits and the available planning time are respected. Experiments are performed in a simulation environment, where the optimal trajectories are executed, highlighting the resulting performances and improvements with respect to non-optimized solutions.