# Control System Design and Methods for Collaborative Robots: Review
## 5 Control Methodologies
### Probabilistic Method  
Several probabilistic techniques have been proposed for translating human intentions. For instance, the authors discussed the human intention estimation problem and proposed a prediction mechanism for online trajectory planning using a hidden Markov model (HMM) algorithm in [38; 78]. The walking human's current position and desired position are used to adjust the robotic movements in industrial application for the collaborative assembly, where the three types of human-robot interactions (coexistence, cooperation, and collaboration) are considered. Each motion pattern \(\theta_{m}\) is described by a set of Gaussian distributions with the coordinate mean \(\mu_{m}^{k}\) and its covariance \(\Sigma_{m}^{k}\sigma\). In the first phase, online trajectory prediction is performed for each observed human position with \(K\) discretized states along with \(M\) motion patterns applying a hidden Markov model (HMM). During the next phase, the probability of each estimated human state \(P(\mu_{m}^{k}\mid\pi_{i})\) is calculated according to  
\[P(\mu_{m}^{k}\mid\pi_{i})=\frac{1}{\sqrt{2\pi\sigma}}e^{\frac{1}{2\sigma^{2}} \mid\pi_{i}-\mu_{m}^{k}\mid^{2}}P^{-}(\mu_{m}^{k}) \tag{19}\]  
The probability of each state is modified during the observation process based on the current state \(P^{-}(\mu_{m}^{k})\) and the observed location of human \(\pi_{i}=(x_{i},y_{i})\).  
When the person at a specific time \(t\) in the future visited an interaction area \(A_{j}\), then the Bayes theorem defines the probability of interaction area \(P(A_{j},t\mid\pi_{i})\) as  
\[\begin{split} P\big{(}A_{j},t\mid\pi_{i}\big{)}&= \sum P\Big{(}A_{j},t,\mu_{m}^{k}\mid\pi_{i}\Big{)}\\ &=\sum P\Big{(}A_{j},t\mid\mu_{m}^{k},\pi_{i}\Big{)}P\Big{(}\mu_ {m}^{k}\mid\pi_{i}\Big{)}\end{split} \tag{20}\]  
The experiments showed successful results when the intention estimation algorithm was tested for coexistence, cooperation, and collaboration scenarios in predicting the correct interaction zone between a robot and human. [PERSON] et al. also suggested an HMM-based approach for predicting the efficient generation of the safety-critical regions occupied by the movement of a human arm over a long-term prediction horizon for planning a robot's motion planning [38]. This probabilistic method uses stochastic transitions between various motion patterns and resolves the uncertainties in the prediction of human movement.  
Classical estimation techniques and deterministic methods produce satisfactory short-term predictions but fail to work well on a long prediction horizon [79; 80]. The research focuses on communicating more human motion information to the robot to make the system efficient and replan its trajectories [81]. While prediction has been shown to be helpful for ensuring safe HRC, the appropriate predictors for a given task and environment are essential to determine the accuracy of the relevant predictors. The results reported that low-confidence task-level predictors into motion-level prediction could deteriorate the prediction performance [82]. Furthermore, one can use control-based safety methods to handle incorrect predictions.