The general stochastic optimal control (SOC) problem in robotics scenarios is often too complex to be solved exactly and in near real time. A classical approximate solution is to first compute an optimal (deterministic) trajectory and then solve a local linear-quadratic-gaussian (LQG) perturbation model to handle the system stochasticity. We present a new algorithm for this approach which improves upon previous algorithms like iLQG. We consider a probabilistic model for which the maximum likelihood (ML) trajectory coincides with the optimal trajectory and which, in the LQG case, reproduces the classical SOC solution. The algorithm then utilizes approximate inference methods (similar to expectation propagation) that efficiently generalize to non-LQG systems. We demonstrate the algorithm on a simulated 39-DoF humanoid robot.

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Robot trajectory optimization using approximate inference

M. R. Hestenes London: John Wiley. 1967. Pp. xii + 405. Price £5. Professor Hestenes has been a leading researcher on optimization theory since the early 1930's and this book contains much of his original work in the field. The first three chapters are of an introductory nature and contain the classical, calculus of variations, approach of first and second variations.

Calculus of Variations and Optimal Control Theory

In this paper, we propose a novel method to generate optimal robot motion based on a sequence of attractor dynamics in task space This is motivated by the biological evidence that movements in the motor cortex of animals are encoded in a similar fashion- and by the need for compact movement representations on which efficient optimization can be performed We represent the motion as a sequence of attractor points acting in the task space of the motion Based on this compact and robust representation, we present a scheme to generate optimal movements Unlike traditional optimization techniques, this optimization is performed on the low-dimensional representation of the attractor points and includes the underlying control loop itself as subject to optimization We incorporate optimality criteria such as eg the smoothness of the motion, collision distance measures, or joint limit avoidance The optimization problem is solved efficiently employing the analytic equations of the overall system Due to the fast convergence, the method is suited for dynamic environments, including the interaction with humans We will present the details of the optimization scheme, and give a description of the chosen optimization criteria Simulation and experimental results on the humanoid robot ASIMO will underline the potential of the proposed approach

https://ipvs.informatik.uni-stuttgart.de/mlr/papers/07-toussaint-Humanoids.pdf

Optimization of sequential attractor-based movement for compact behaviour generation

An apparatus and a method for optimizing robot performance includes a computer connected to the robot controller for receiving performance data of the robot as the controller executes a path program. The computer uses the performance data, user specified optimization objectives and constraints and a kinematic/dynamic simulator to generate a new set of control system parameters to replace the default set in the controller. The computer repeats the process until the new set of control system parameters is optimized.

A Method for Optimizing a Robot Program and a Robot System

A robot is provided with a motion control unit that avoids collision between segments of the robot or between segments of the robot and other objects. The motion control unit of the robot comprises a distance computing module, a whole body control module, a collision avoidance module, and a blending control unit. The distance computing module calculates two closest points of different segments of the robot connected to each other via at least one joint or a segment of the robot and another object. The collision avoidance module is provided with the information about the two closest points. The blending control unit combines the weighted output control signals of the whole body control module and the collision avoidance control module. The weight of the whole body control output signal is higher when the risk of collision is lower. The weight of the collision avoidance control output signal is higher when the risk of collision is higher. The collision avoidance module is designed to control a collision avoidance action only in the direction parallel to a line connecting between the two closest points.

Robots with collision avoidance functionality

Real-time collision-free trajectory control is dealt with by semi- infinite optimization techniques. This allows an optimal control problem incorporating a robotlobstacle distance function for col lision detection to be reduced to a finite-dimensional parameter- optimization problem. This reduced problem can be solved effi ciently by the numerical parameter-optimization method of sequen tial quadratic programming. In the case of a time-varying robot environment, a series of such optimization problems is solved in an iterative time frame, constituting a real-time optimization loop.

M. Schlemmer

Papers

Real-Time Collision- Free Trajectory Optimization of Robot Manipulators via Semi-Infinite Parameter Optimization