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... Dynamics’s LittleDog (left), and Barrett Technology’s WAM arm (right). obstacles are framed in terms of mixed integer programming, which is known to be an NP-hard problem (Schouwenaars et al., 2001; =-=Earl et al., 2005-=-; Ma et al., 2006; Vitus et al., 2008). Approximately optimal algorithms exist, but so far, they only consider very simple obstacle representations (Sundar et al., 1997). In the rest of this chapter, ...

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... as the number of nodes in the solution tree grows exponentially with the number of binary variables. Some heuristic solutions related to this for cooperative vehicles are presented in [28]. See also =-=[29]-=- for an iterative MILP algorithm that use fewer binary variables than standard MILP methods, and require less computational effort. A different strategy to deal with the computational complexity of pa...

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... include quadrotors and carlike vehicles. It is well-known that mixed-integer linear programming can be used for reasoning about propositional logic [8, 12], generating state-constrained trajectories =-=[9, 21, 24]-=-, and modeling vehicle routing problems [14, 23]. The work most similar to ours is Karaman et al. [16], who consider controller synthesis for MLD systems subject to finite-horizon LTL specifications. ...

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...the minimum-control-effort trajectory-generation problem with those obtained by directly using the COIN-OR solver within the framework of the iterative MILP time-step selection algorithm presented in =-=[6]-=-. 50 random instances of the problem are generated with the same parameter ranges as given in [6] and the last 10 instances are used for testing whereas all the others are utilized for learning. Table...

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...equivalent to piecewise affine systems [6]. It is wellknown that mixed-integer linear programming can be used for reasoning about propositional logic [8, 14], generating stateconstrained trajectories =-=[11, 22, 25]-=-, and modeling vehicle routing problems [16, 24]. The work most similar to ours is Karaman et. al. [17], who consider controller synthesis for MLD systems subject to finite-horizon LTL specifications....

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...uent planning iteration admits a feasible solution. One way to mitigate this issue is to incorporate terminal constraints for each planning iteration to ensure continued feasibility of path solutions =-=[15]-=-. Implementing safety constraints in the MILP formulation is a future direction for this work. In the fixed horizon strategy, in addition to high computational complexity, another drawback is poor rob...

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...ve to create for high-dimensional manipulators [25]. Many optimal controllers which do handle obstacles are framed in terms of mixed integer programming, which is known to be an NP-hard problem [24], =-=[9]-=-, [17], [27]. Approximately optimal algorithms exist, but so far, they only consider very simple obstacle representations [26]. In the rest of this document, we give a detailed derivation of the CHOMP...

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...lem. These variables can be used to represent logical constraints such as obstacles and collision avoidance rules, while the dynamic properties of the vehicle are formulated as continuous constraints =-=[18]-=-[79]. Although MILP can systematically handle obstacle and collision constraints, it cannot handle the computational complexity of a typical planning problem. Online optimization of a less general pro...

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... optimization problem with the robot dynamics as constraints and solved using techniques such as mixed integer linear programming, nonlinear programming, and other constrained optimization techniques =-=[51, 52, 53, 54]-=-. In model predictive control, the trajectory planning problem is posed again as an optimization problem, but optimized over finite 5horizon. This way the solution obtained is suboptimal but takes le...