# Kinematic Tripod (K3P): A New Kinematic Algorithm for Gait Pattern Generation
## 6 Conclusions  
In this article, the K3P algorithm is proposed as a novel approach for dynamic gait generation for hexapod robots. This new algorithm is based on a kinematic planner for the legs organized as tripods. The core of K3P are three shift phase conditions, K3P\({}_{1,2,3}\), that ensure the static slip-free stability of the robot throughout its operation, without requiring any precomputed paths or trajectories whatsoever. The methodology and numerical results are presented for a radial hexapod traversing a lemniscate trajectory, shown as a versatile methodology when commanding an hexapod. Compared to other approaches, K3P does not require any precomputed information from the trajectory to be followed, nor the trajectory for every support point \(SP_{i}\), nor precomputed gait patterns. Instead, all trajectories for every tripod were dynamically generated in real-time and made possible that \(B\) described a smooth arbitrary trajectory at an arbitrary velocity while the support points remained still over the uneven surface that the robot was walking on. Additionally, K3P is able to dynamically change the clearance of the robot, and we studied the trade-off between clearance vs. step length, given the physical dimensions of the robot. \begin{table}
\begin{tabular}{l l l l} \hline \multicolumn{4}{c}{**Mass Distribution of the Robot**} \\ \hline
**Qty.** & **Link** & **Unit Mass [gr]** & **Subtotal** \\ \hline
1 & Main body & 640 & 640 \\
6 & Coxa & 80 & 480 \\
6 & Femur & 53 & 318 \\
6 & Tibia & 26 & 156 \\ \hline \multicolumn{4}{c}{Total weight} & 1594 \\ \hline \end{tabular}
\end{table} 
Table 5: Discrete masses that form the robot. Figure 9: The trajectories of \(SP_{1}\) when K3P drives the hexapod uphill (black solid line) at two different settings for the maximum height. The hexapod robot moves from left to right, the trajectory of \(B\) is also shown. For simplicity, we only show the trajectory for leg number 1. (**a**) The limbs are swinging at 50% of clearance. (**b**) The limbs are swinging at 90% of clearance. The K3P algorithm is executable on commercially available embedded computers, using fast linear algebra computation libraries, such as Lapack. Modern CPUs support instruction sets enabling parallelization, such as Single Instruction Multiple Data (SIMD), while GPUs can further enhance the algorithm's execution speed. The possibility of implementing the algorithm on an FPGA can also be considered. Consequently, K3P algorithm finds application in real-time scenarios for robot control. However, it can also be utilized in offline contexts. For example, K3P could serve as a teaching tool for neural networks, with K3P criteria employed to reinforce the learning process of walking. Because the K3P algorithm performs at real-time and under static stability, it can change the direction of movement of the robot at any given moment. This can be useful if the robot performs in an ever-changing environment with static and dynamic obstacles, e.g., humans or other mobile robots. Such is the case in collaborative robotics; in this emerging research field, robots perform alongside humans or other robots [25]. K3P can offer a development opportunity in collaborative robotics because it can make the robot stop or perform an immediate change in direction of movement when close to a moving obstacle or in a dangerous situation. The viability of the algorithm is proven by estimating the torques exerted on the knee and lift joints, which are below the maximum torque of commercially available electric servo motors. As it was shown in the previous section, the K3P algorithm can drive a hexapod robot over irregular terrain without planning in advance every step of the robot at an arbitrary speed. This key design choice for K3P has an important implication: a higher-level trajectory planner can determine the most suitable path for the robot to follow, so that all traversed portions of the terrain can support a footstep.