Prioritized Optimal Control

Pre-print of the paper presented at Robotics and Automation (ICRA), IEEE International Conference on, Hong Kong, China, 2014This paper presents a new technique to control highly redundant mechanical systems, such as humanoid robots. We take inspiration from two approaches. Prioritized control is a widespread multi-task technique in robotics and animation: tasks have strict priorities and they are satisfied only as long as they do not conflict with any higher-priority task. Optimal control instead formulates an optimization problem whose solution is either a feedback control policy or a feedforward trajectory of control inputs. We introduce strict priorities in multi-task optimal control problems, as an alternative to weighting task errors proportionally to their importance. This ensures the respect of the specified priorities, while avoiding numerical conditioning issues. We compared our approach with both prioritized control and optimal control with tests on a simulated robot with 11 degrees of freedom

Automating control system design via a multiobjective evolutionary algorithm

This chapter presents a performance-prioritized computer aided control system design (CACSD) methodology using a multi-objective evolutionary algorithm. The evolutionary CACSD approach unifies different control laws in both the time and frequency domains based upon performance satisfactions, without the need of aggregating different design criteria into a compromise function. It is shown that control engineers' expertise as well as settings on goal or priority for different preference on each performance requirement can be easily included and modified on-line according to the evolving trade-offs, which makes the controller design interactive, transparent and simple for real-time implementation. Advantages of the evolutionary CACSD methodology are illustrated upon a non-minimal phase plant control system, which offer a set of low-order Pareto optimal controllers satisfying all the conflicting performance requirements in the face of system constraints

Towards Task-Prioritized Policy Composition

Combining learned policies in a prioritized, ordered manner is desirable because it allows for modular design and facilitates data reuse through knowledge transfer. In control theory, prioritized composition is realized by null-space control, where low-priority control actions are projected into the null-space of high-priority control actions. Such a method is currently unavailable for Reinforcement Learning. We propose a novel, task-prioritized composition framework for Reinforcement Learning, which involves a novel concept: The indifferent-space of Reinforcement Learning policies. Our framework has the potential to facilitate knowledge transfer and modular design while greatly increasing data efficiency and data reuse for Reinforcement Learning agents. Further, our approach can ensure high-priority constraint satisfaction, which makes it promising for learning in safety-critical domains like robotics. Unlike null-space control, our approach allows learning globally optimal policies for the compound task by online learning in the indifference-space of higher-level policies after initial compound policy construction

Blamelessly Optimal Control For Polytopic Safety Sets

In many safety-critical optimal control problems, users may request multiple safety constraints that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we introduce the concept of blameless optimality to characterize control actions that a) satisfy the highest prioritized and feasible safety constraints and b) remain optimal with respect to a mission objective. For a general optimal control problem with jointly infeasible safety constraints, we prove that a single optimization problem cannot find a blamelessly optimal controller. Instead, finding blamelessly optimal control actions requires sequentially solving at least two optimal control problems: one to determine the highest priority level of constraints that is feasible and another to determine the optimal control action with respect to these constraints. We apply our results to a helicopter emergency landing scenario in which violating at least one safety-induced landing constraint is unavoidable. Leveraging the concept of blameless optimality, we formulate blamelessly optimal controllers that can autonomously prioritize human safety over property integrity

Prioritized motion-force control of constrained fully-actuated robots: "Task Space Inverse Dynamics"

Pre-print submitted to "Robotics and Autonomous Systems"We present a new framework for prioritized multi-task motion-force control of fully-actuated robots. This work is established on a careful review and comparison of the state of the art. Some control frameworks are not optimal, that is they do not find the optimal solution for the secondary tasks. Other frameworks are optimal, but they tackle the control problem at kinematic level, hence they neglect the robot dynamics and they do not allow for force control. Still other frameworks are optimal and consider force control, but they are computationally less efficient than ours. Our final claim is that, for fully-actuated robots, computing the operational-space inverse dynamics is equivalent to computing the inverse kinematics (at acceleration level) and then the joint-space inverse dynamics. Thanks to this fact, our control framework can efficiently compute the optimal solution by decoupling kinematics and dynamics of the robot. We take into account: motion and force control, soft and rigid contacts, free and constrained robots. Tests in simulation validate our control framework, comparing it with other state-of-the-art equivalent frameworks and showing remarkable improvements in optimality and efficiency