A grid maze is a binary matrix where fields containing a 0 are accessible while fields containing a 1 are blocked. A movement sequence consists of relative movements up, down, left, right – moving to a blocked field results in non-movement. The simultaneous maze solving problem asks for the shortest movement sequence starting in the upper left corner and visiting the lower right corner for all mazes of size n × m (for which a path from the upper left to the lower right corner exists at all). We present a theoretical problem analysis, including hardness results and a cubic upper bound on the sequence length. In addition, we describe several approaches to practically compute solving sequences and lower bounds despite the high combinatorial complexity of the problem.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.