# An Efficient Stochastic Constrained Path Planner for Redundant Manipulators
## 5 Results
### Real Experiments  
An experiment has been conducted on a physical manipulator to verify the performance of the proposed method under realistic settings. Figure 3 presents the real experimental setup with the 7R Rethink Robotics Sawyer cobot. The experiment consists of tracking a reference linear path on a flat surface whilst keeping the tool in an orientation perpendicular to the surface throughout the motion. A force controller developed to maintain contact with the surface was implemented [18] to aid with the task at hand of simulating a surface conditioning assignment such as polishing, whilst the pose adopted along the path is set by the proposed SCO path planning strategy. The experimental setup is depicted in Figure 3a, consisting of a 7R Rethink Robotics Sawyer cobot, a force sensor Nano25 SI-25-25 attached to the robot end-effector, a small polishing tool proxy attached to the sensor (a cylinder of 43 \(\times\) 43 \(\times\) 10 mm), and a target flat surface to polish.  
As per the test methodology adopted in the simulation cases to show the capabilities of the proposed method, the routine undertaken includes a comparison with the standard \"Simple Planner\" derived from the the Moore-Penrose solution (Algorithm 2). The initial conditions are set to be the same in both cases: an obstacle-free initial pose with average manipulability established prior. This was the initial condition fed to both trajectory planners. A video is supplied ([[https://arvc.umh.es/arte/AppliedSciences21.mp4](https://arvc.umh.es/arte/AppliedSciences21.mp4)]([https://arvc.umh.es/arte/AppliedSciences21.mp4](https://arvc.umh.es/arte/AppliedSciences21.mp4)), accessed on 11 November 2021) to visualise the full experimental setting and resulting motion, with several stills depicting the starting, mid- and end-points of the test trajectories also being collected in Figure 3. It can be observed how the optimality in manipulability being sought out by the SCO proposed planners derives configurations that keep the elbow link down, whereas in the \"Simple Planner\" case that is not the case, ultimately even compromising stability by traversing near-singular regions. The reader is referred to the video linked in the manuscript where the undesirable dynamic disturbances induced in the controller are clearly apparent with vibrations at compromised locations along the path, most notably at the mid-point (Figure 3e).  
The final manipulability attained in both instances, shown in Figure 4, corroborates the ability of the algorithm to seek areas with higher manipulability, hence permitting operations with manipulator configurations away from singularity regions, ultimately leading to superior end-effector precision, less energy expenditure and overall safer trajectories whilst seeking to abide by the desired end effector path during execution.  
Figure 3: Sawyer polishing task experiment: (**a**) setup: 7R manipulator with a force sensor attached to the robot end-effector, a tool consisting of a cylinder of 43 \(\times\) 43 \(\times\) 10 mm attached to the sensor and a flat surface target, (**b**) initial pose with minimal manipulability for both tests, (**c.d**) proposed SCO algorithm, (**e.f**) “Simple Planner” case.