Globally Convergent Optimal Dynamic Inverse Kinematics for Distributed Modular and Self-Reconfigurable Robot Trees

Kinematic trees of self-reconfigurable, modular robots are difficult to control for at least three primary reasons: (1) they must be controlled in a distributed fashion, (2) they are often kinematically redundant or hyper-redundant, and (3) in many cases, these robots must be designed to safely operate autonomously in dangerous and isolated environments. Much work has been done to design hardware, distributed algorithms, and controllers to handle different aspects of this challenging problem, but the design of generalized and globally optimal inverse kinematics algorithms for such systems is largely an open problem. Jacobian-based methods have welldocumented shortcomings, particularly for high-DOF systems, while alternative methods, such as those based on genetic and evolutionary algorithms, provide no guarantees of convergence to a globally optimal solution. Such a guarantee is particularly important in the types of dangerous environments in which these robots are to operate. This paper proposes a novel distributed inverse kinematics framework based on the recently proposed Branch and Bound Particle Swarm Optimization (BBPSO) algorithm, which provably converges to a globally optimal solution (and converges in finite time given any positive error tolerance). This framework is demonstrated, through extensive simulations, to offer high-quality solutions in practical amounts of time, even for multi-effector and dynamic problems, such as those encountered in kinematic self-reconfiguration where the effector workspace goal pose is not available as input.