### Table 8.1 The coherence between the features and the objects in their environment for robot r1 after 42 discrimination games. Charging station Competitor Robot

### Table 1. Example of specification of the a robot is returning uselessness NCS.

"... In PAGE 6: ...lockage. If it is possible, r1 moves to its sides (an is no more returning). Else, r1 moves forward until it cannot continue or if encounters another robot r2 which is returning and is closer to its goal than r1. Table1 sums up the behavior in this situation. If there is a line of robot, the first returning robot is seen by the second one that will return too.... ..."

### Table 1: Optimal plan for the mail delivery problem (Robot 1)

"... In PAGE 4: ...ne of the optimal solutions (w.r.t. the overall number of actions) for this problem consists of three parallel sequences of ordered actions, each sequence being a the set of actions to be executed by one of the robots ( Table1 , 2, 3). Another solution would be to send R1 to transport C1 and robot R2 or R3 to deliver firstly C2 and C3 afterwards.... ..."

### TABLE 1 D-H Parameters for a 4R Robot Joint Offset d

### Table 1: Sensitivity of learned skill w.r.t. changes in the robot apos;s position and orientation. x; y; and denote the changes, quot;Cycles quot; is the number of control cycles until termina- tion, quot;Term quot; denotes the termination condition (E = error condition was detected, A T = user abort because of termination condition, T = termination condition was detected).

"... In PAGE 18: ... In addition, the goal direction detection system2 returns the number #p of the most active photosensor. For the neural controller a normalized scalar t is used to indicate the direction to the goal according to the rules given in Table1 . The control variables of the robot are the change of the heading direction t in degrees/s and the speed of the movement vt in inches/s.... In PAGE 19: ... The value of M is determined according to the photosensor number #p which is returned by the goal direction detection system. Table1 shows the rules of the MOVE-TO-GOAL re ex for determining the value for M (in degrees/s). Finally, the RETRACT re ex tries to recover from physical or immediate collisions by recommending a moving speed vR.... In PAGE 19: ...5 15 3 1 30 4 -1 -30 5 0 0 6 1 30 7 -1 -30 8 1.5 45 Table1 : Rules for determining the values for and M as a function of the photosensor number #p. AVOID-OBSTACLES re ex: IF (r4 lt; 15 OR r3 lt; 15 OR r5 lt; 15) THEN IF r3 lt; r5 THEN A = ?30 ELSE A = 30 ELSE IF (r2 lt; 15 OR r6 lt; 15) THEN IF r2 lt; r6 THEN A = ?20 ELSE A = 20 ELSE IF (r1 lt; 15 OR r7 lt; 15) THEN IF r1 lt; r7 THEN A = ?10 ELSE A = 10 ELSE A = 0 Figure 10: Rules of the AVOID-OBSTACLES re ex to determine the value for A.... ..."

### Table 3.5a: Irreducible representations of SL(2; Zp) for p 6 = 2

"... In PAGE 58: ...s given in Table 4.4 below. We shall show that by property (1) to (5) the representation is uniquely de- termined (up to equivalence). Its precise description can be read o from the last column of Table3 , respectively (notations will be explained below). In particular, has dimension equal to the cardinality of Hc, and hence we conclude H = Hc.... In PAGE 61: ...4. We now consider the rational models corresponding to row 5 to 9 of Table3 . Here the level of e is a prime l, the dimension of is l ? 1, and the eigenvalues of (T ) are pairwise di erent primitive l-th roots of unity.... ..."

### Table 3.5a: Irreducible representations of SL(2; Zp) for p 6 = 2

"... In PAGE 58: ...s given in Table 4.4 below. We shall show that by property (1) to (5) the representation is uniquely de- termined (up to equivalence). Its precise description can be read o from the last column of Table3 , respectively (notations will be explained below). In particular, has dimension equal to the cardinality of Hc, and hence we conclude H = Hc.... In PAGE 61: ...4. We now consider the rational models corresponding to row 5 to 9 of Table3 . Here the level of e is a prime l, the dimension of is l ? 1, and the eigenvalues of (T ) are pairwise di erent primitive l-th roots of unity.... ..."

### Table 1: Robot navigation instances

2005

"... In PAGE 10: ... Table1 summarizes the robot instances. The second column in Table 1 indicates if the instance has a solution.... In PAGE 13: ... Due to the transformation, the number of variables and clauses increases substantially. For example, the Q-ALL SAT instance robot 8 1 has according to Table1 a total of jQj + jXj + jY j = 256 variables, a total of 1521 clauses in R and S, and 925 clauses in R. The corresponding instance in the Q-DIMACS format has 256 + 925 + 1 = 1182 variables and 3211 clauses.... ..."

Cited by 6

### Table 6.4 In this example, as was the case in all multi-parameter, higher dimensional examples we studied, the SPL schemes performed iar better than the AVE. In fact, even for large values of N, it was not uncommon for the SPL schemes to converge while the AVE schemes did not. In all examples studied, for N sufficiently large, the SPL based schemes would always produce a solution to the approximating parameter identification problem. Moreover, as N increased, the solutions to the approximating problems appeared to be converging to the true parameter values used to generate the observational data.

1981

### Table 2: Results for the symmetric algorithm Of course the average time needed by n robots (t = d=n) searching with the symmetric algorithm is easily deduced thanks to the results above, and are given in Table 2. As we can see, for example, for n = 10 the parallel search of a line at unit distance is very close to the limit 1. 4 Searching for a line at an arbitrary distance When the line is at an unbounded distance the best known algorithm for one robot is to follow a logarithmic spiral with radius r( ) = k with k 1:250, which gives a worst case asymptotic ratio between the distance travelled to the line distance of 13.81. For n gt; 2 robots we can use the symmetric algorithm of the previous section, obtaining the same results, because they do not depend on the distance to the line. So the distance travelled 8

"... In PAGE 8: ... When a robot R nds the line, the other have walked n ? 1 times the distance travelled by R. The probability that none of the robots have found the line when a robot nds it, in function of the angle covered is p( ) = 1 ? n That average distance walked for that robot is then d1 = 1 + Z n ? n p( ) 1 cos ? 1 d 2 = 1 ? 1 n + 1 ln(tan( 4 + 2n)) With n robots, the average (total) distance travelled is therefore given by: d = nd1 = n ? 1 + n ln(tan( 4 + 2n)) = n + 2 6n2 + O(n?4) Numerical evaluation with Maple gives the results shown in Table2 , giving for completeness also... ..."