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19

As far as I know, this problem hasn't been "solved." Formally, this is an online coverage problem. Coverage, because we must cover each point on the floor, and online because we do not have offline access to the map. If you are interested in the most recent results, I suggest you lookup "robotic online coverage algorithms," perhaps in google scholar (there ...

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Roomba starts in a spiral until it hits something, then does a perimeter sweep. Then it just bounces around. Roomba being the de facto standard in household robotic vaccum cleaners, I guess you could call it the "accepted solution". But from personal experience (I own two), there is definitely room for improvement. From How Stuff Works: From an interview ...

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You're making two mistakes that I can see, both related to the idea of "shrinking" the set of front or back wheels into a single wheel. Rather than thinking of Ackermann steering as (conceptually) a single wheel, imagine expanding the single front wheel of a tricycle into 2 wheels. At first, the tire gets wider, then splits into two tires, then they get ...

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Neato uses an organized approach. Using SLAM and bumpers, it maps the 'current' room, perimeter first, then applies some algorithm for cleaning as efficiently as possible. I've never owned a Roomba, but given what I have read about it's algorithm, I would never switch from a neato. The Laser Range Finder in the neato is often cannabilized for robotics, as ...

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Given that an homogeneous transformation $T \in SE\left(3\right)$ can be expressed as $$T= \left( \begin{matrix} \mathbf{R} & \mathbf{p} \\ 0 & 1\end{matrix} \right),$$ where $\mathbf{R} \in \mathbb{R}^{3 \times 3}$ is symmetric and $\mathbf{p} \in \mathbb{R}^{3 \times 1}$, then we seek for the inverse $T^{-1}$, such that: $$T^{-1}=\left( \begin{... 6 The first thing you need to establish is the goal of the robot -- not quite clear from your question. There are two main tasks that your robot has to accomplish: discovering the shape of the clean-able area, and then cleaning it. But is the amount of dirt constant? Is dirt added constantly? Is it your goal to minimize the average time that dirt remains ... 5 Specifically, the Chi-Square Distribution(or Chi2, \chi^2, or equivalently \chi^2_1) is used to model the probability of the absolute value of the deviation of the measurement from it's expected value. This calculation is vital to tackle the measurement origin uncertainty problem. It can also be used to determine the "correctness" of a multi-hypothesis ... 5 A hint towards what the answer is given in the paper. Namely, one can use the generalized eigenvalue decomposition, which in this case can be formulated as finding eigenvalues \lambda \in \mathbb{R} and eigenvectors v \in \mathbb{R}^n such that$$ (\lambda\,\Lambda - K_d)\,v = 0. \tag{1} $$Consider two distinct solutions (\lambda_i,v_i) and (\... 4 *Note, a|b is the concatenation of paths a and b. Then c(\cdot) defined as the minimum clearance implies c(a|b)=min(c(a),c(b)) You refer to (in reference 1): Theorem 11: (Additivity of the Cost Function.) For all \sigma_1,\sigma_2 \in X_{free} , the cost function c satisﬁes the following: c(\sigma_1|\sigma_2) = c(\sigma_1) + c(\... 4 \mu_{t-1} is the state estimate from the last time step, x_{t-1} is the actual state (a random variable) in the last time step. Basically it goes like this: in the traditional Kalman filter, you have linear models that tells us how states evolve and measurements are made. In the EKF you have non-linear models but want to use the Kalman filter equations,... 4 I will try to make it as simple as possible. Imagine you have a SCREW, when you WRENCH it, it TWIST forward or backward. From your wiki link The components of the screw define the Plücker coordinates of a line in space and the magnitudes of the vector along the line and moment about this line. It means that any system can be described as those ... 4 A model of the environment in this context is an abstraction of the real world, which should be adequate for the task of the robot. For example, if you have a robot that needs to navigate an office building, you can make the abstraction that your model only needs to be in two dimensions. Further, for the task of navigation you could discretize your space in ... 3 The way you are describing it, DOM is the number of independent dimensions in \vec q. DOF is the number of independent dimensions in \vec x. In practice, a robotics engineer will use DOF to represent the number of independent actuators of the robot, which you are calling DOM. Better notation would be to call DOM the mobility of the system, as ... 3 Complexity is not a word that's used in control theory but I think I know what you mean. The short answer would be no. Complexity in systems to be controlled is usually looked at in terms of how many state variables are needed to fully describe what's happening or, more often, how many Degrees of Freedom exist. There is a theorem that says whether a Linear ... 3 After the propagation step, we need to find the parameters of the Gaussian which describe our new estimate. These are, the mean \mu, and the co-variance \Sigma. You asked about the mean specifically, so here we go. Note that the definition of the mean of the propagated state is the expectation of the propagated state. Taking the expectation of the ... 3 You are correct in that there is no Kinematic difference. Kinematics do not consider why things happen - ie dynamic stability. There are obvious physical differences, but when the math is worked out for kinematics, it should be the same. This of course implies a certain realistic cap on the level of kinematics. For example it has been pointed out a ... 2 I'm not sure if you still need it, but for those who happened to google for this thread, I have made one simple version of the algorithm. Basically, it tries to build the map of the area while it cleans, and it uses the map to find the nearest unvisted node (part of the room). When it can't find any, that means the room is cleaned (or the uncleaned parts ... 2 RoboEarth was the name of a European project. Knowrob is software that was developed, in part, by the RoboEarth project. 2 I'll just show why heuristics and experience are relevant in this problem by showing that is nearly impossible to solve optimally. Note, genetic algorithms cannot necessarily always solve a problem optimally, they are just another heuristic-based search. Defining the manipulator Let's simplify things. According to Craig 2005, robot manipulators can be ... 2 It's usually best to contact the author directly if you have a specific question about a specific paper. The simulations are there only to illustrate the principal of the passivity observer and controller, so it makes sense they did not elaborate on them too much. The first simulation uses velocity and position as the input and appears to have an initial ... 2 Fuzzy logic is definitely used in many of the control systems including but not limited to robotics. See this paper for an example: https://pdfs.semanticscholar.org/b9a7/332b03d46b3ee08b9d113e64714e6b668601.pdf and this: https://ieeexplore.ieee.org/document/1678143 If we consider fuzzy logic as dubious then we should do the same to probabilities. Both ... 2 Short answer: Fuzzy logic (FL) isn't applicable for robotics research, The long answer is, that in the 1980s as part of the fifth computer generation fuzzy logic was researched in Japan with the attempt to build intelligent advanced parallel computers, but the Japanese researchers have failed. Fuzzy logic isn't a technical idea but a philosophical ... 2 I would like to mention that Fuzzy logic is still an active control system used in many industry applications. In garbage fired power plants, concrete aggregate firing, hydraulics, and the control of flow of powdered 'fluids' in foundries to name a few. However, I will admit, I've only seen them used in 'one off' difficult to model projects, such as power ... 2 A definition of the cross product for quaternions is$$p \times q = \frac{1}{2}(pq - qp)$$We also have the identity (3.167) in Jazar$$pq = -p \cdot q + p \times q$$Apparently the vectors  \dot{e}\overset{\ast}{e}  and {}^Gr are orthogonal, so their dot product is zero and we have:$$\dot{e} \overset{\ast}{e}{}^Gr = \dot{e} \overset{\ast}{e} \times {...

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I would say the transferfunction becomes $\frac{1}{s^2}$ iff you assume you have a perfect drive without any dynamics. Since this system is unstable you have to be careful choosing your controllers. The best way in my opinion is to use a standard state feedback controller (LQR, Ackermann). The huge advantage using state feedback is that you can chose the ...

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Appending to @WalterJ's answer. Linear and nonlinear systems which form the basis for subjects like optimal control theory have rigorous math fundamentals which allow you to analyze ODEs without actually solving them and mathematically prove whether is system is stable, how fast your convergence will be or define a safe operating region. This makes ...

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The reason why ODE's are used is simply: physics. It would be great if any system could be modelled by a simple linear function like $x(t)=at$, but nature is not so simple, or linear. Even when you neglect nature, dynamical systems, like $\dot{x}(t)=f(x(t))$ still pop up everywhere, like CroCo said, it is the basis of the mathematical modelling of many ...

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You might like the algorithms run on PR-2 robot. Two papers I can think of are "A single planner for a composite task of approaching, opening and navigating through non-spring and spring-loaded doors" and "Motion planning for smooth pickup of moving objects". Both can be found on IEEE Xplore.

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I went through the Virginia Community College System (VCCS) (not saying which one specifically for myself). In Virginia, if you graduate with >= 3.0 GPA from a Virginia Community College, you are guaranteed admission to any public (Virginia) university. Community colleges here are top notch; I got the most knowledge out of community college courses and grad ...

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Summarizing from Murray, Li, and Sastry (chapters 3 and 5) there are 3 related things: Twist: An element of se(3) (which is a bit like the derivative of an element of SE(3), which is the set of translations + rotations) Screw: A translation+rotation (i.e. and element of SE(3)) Wrench: Generalized force (combination of linear force and torque)

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