# Fast Manipulability Maximization Using Continuous-Time Trajectory Optimization

## TL;DR

This paper introduces a method to maximize manipulability in robotic trajectory planning by representing trajectories as continuous-time Gaussian processes, enabling more agile and adaptable manipulator motions with reduced computational costs.

## Contribution

It presents a novel approach that integrates manipulability maximization into continuous-time trajectory optimization using Gaussian processes, improving agility and safety in manipulation tasks.

## Key findings

- Increased manipulability in simulated and real experiments.
- Maintained smooth and dexterous trajectories.
- Reduced computational cost through sparse GP representation.

## Abstract

A significant challenge in manipulation motion planning is to ensure agility in the face of unpredictable changes during task execution. This requires the identification and possible modification of suitable joint-space trajectories, since the joint velocities required to achieve a specific endeffector motion vary with manipulator configuration. For a given manipulator configuration, the joint space-to-task space velocity mapping is characterized by a quantity known as the manipulability index. In contrast to previous control-based approaches, we examine the maximization of manipulability during planning as a way of achieving adaptable and safe joint space-to-task space motion mappings in various scenarios. By representing the manipulator trajectory as a continuous-time Gaussian process (GP), we are able to leverage recent advances in trajectory optimization to maximize the manipulability index during trajectory generation. Moreover, the sparsity of our chosen representation reduces the typically large computational cost associated with maximizing manipulability when additional constraints exist. Results from simulation studies and experiments with a real manipulator demonstrate increases in manipulability, while maintaining smooth trajectories with more dexterous (and therefore more agile) arm configurations.