We propose a learning framework, named Multi-Coordinate Cost Balancing (MCCB), to address the problem of acquiring point-to-point movement skills from demonstrations. MCCB encodes demonstrations simultaneously in multiple differential coordinates that specify local geometric properties. MCCB generates reproductions by solving a convex optimization problem with a multi-coordinate cost function and linear constraints on the reproductions, such as initial, target, and via points. Further, since the relative importance of each coordinate system in the cost function might be unknown for a given skill, MCCB learns optimal weighting factors that balance the cost function. We demonstrate the effectiveness of MCCB via detailed experiments conducted on one handwriting dataset and three complex skill datasets.
The motion planning framework in @cite_13 , complementary to our approach, utilizes a blended cost function, the construction of which is guided by probability distributions learned from the demonstrations. This framework incentivizes factors such as smoothness, manipulability, and obstacle avoidance, but is restricted to the Cartesian coordinate system. MCCB, on the other hand, encodes demonstrations in multiple differential coordinates and learns to optimally balance their relative influences, but does not consider factors such as manipulability and obstacle avoidance.
@cite_13
2494937121 2019965290 2103052138 2201235033
In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective Planning) algorithm for addressing the stochastic kinodynamic motion planning problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject to a constraint on collision probability (CP). To ensure exhaustive evaluation of candidate motion plans (as needed to tradeoff the competing objectives of performance and safety), PUMP incrementally builds the Pareto front of the problem, accounting for the optimization objective and an approximation of CP. This is performed by a massively parallel multiobjective search, here implemented with a focus on GPUs. Upon termination of the exploration phase, PUMP searches the Pareto set of motion plans to identify the lowest cost solution that is certified to satisfy the CP constraint (according to an asymptotically exact estimator). We introduce a novel particle-based CP approximation scheme, designed for efficient GPU implementation, which accounts for dependencies over the history of a trajectory execution. We present numerical experiments for quadrotor planning wherein PUMP identifies solutions in 100 ms, evaluating over one hundred thousand partial plans through the course of its exploration phase. The results show that this multiobjective search achieves a lower motion plan cost, for the same CP constraint, compared to a safety buffer-based search heuristic and repeated RRT trials. We present a new approach to motion planning using a stochastic trajectory optimization framework. The approach relies on generating noisy trajectories to explore the space around an initial (possibly infeasible) trajectory, which are then combined to produced an updated trajectory with lower cost. A cost function based on a combination of obstacle and smoothness cost is optimized in each iteration. No gradient information is required for the particular optimization algorithm that we use and so general costs for which derivatives may not be available (e.g. costs corresponding to constraints and motor torques) can be included in the cost function. We demonstrate the approach both in simulation and on a mobile manipulation system for unconstrained and constrained tasks. We experimentally show that the stochastic nature of STOMP allows it to overcome local minima that gradient-based methods like CHOMP can get stuck in. In this paper we address the problem of motion planning in the presence of state uncertainty, also known as planning in belief space. The work is motivated by planning domains involving nontrivial dynamics, spatially varying measurement properties, and obstacle constraints. To make the problem tractable, we restrict the motion plan to a nominal trajectory stabilized with a linear estimator and controller. This allows us to predict distributions over future states given a candidate nominal trajectory. Using these distributions to ensure a bounded probability of collision, the algorithm incrementally constructs a graph of trajectories through state space, while efficiently searching over candidate paths through the graph at each iteration. This process results in a search tree in belief space that provably converges to the optimal path. We analyze the algorithm theoretically and also provide simulation results demonstrating its utility for balancing information gathering to reduce uncertainty and finding low cost paths. In this paper we consider the motion planning problem of humanoid with articulated-spine for object manipulation in double support phase. Complexity of motion planning increases due to higher degrees-of-freedom (DOF), redundancy arising due to articulated spine, inherent underactuation and stability constraint. Additionally, loop-closure constraints arise during double-support phase, and self-collision constraints exist independent of the task to be performed. These problems make motion planning of humanoids a challenging task. In this work, we address the above issues by proposing a sampling based approach for planning the motion of the humanoid. Our approach to the problem is based on RRT* which can generate asymptotically optimal paths. The proposed approach deals with the stability constraints by rejective sampling approach which divides random configurations generated into valid and invalid configurations. Additionally, the loop-closure constraints are tackled by separating the humanoid into two open-kinematic sub-chains, and then generating random configurations in one sub-chain whereas the remaining sub-chain uses inverse kinematics for closure. Efficacy of the proposed approach is demonstrated for whole-body motion planning of a 25-DOF humanoid in generating asymptotically optimal end-effector paths.