Animate a CALayer's position starting from its current (possibly mid-animation) position.

ViewController.m

#import "ViewController.h"
#import <QuartzCore/QuartzCore.h>

@interface ViewController ()

@end

@implementation ViewController {
    CALayer *_layer;
}

static const CGFloat kUpY = 115;
static const CGFloat kDownY = 310;

- (void)viewDidLoad
{
    [super viewDidLoad];

    _layer = [CALayer layer];
    _layer.bounds = CGRectMake(0, 0, 40, 40);
    _layer.backgroundColor = [UIColor redColor].CGColor;
    _layer.position = CGPointMake(50, kUpY);
    [self.view.layer addSublayer:_layer];

    UIButton *button = [UIButton buttonWithType:UIButtonTypeRoundedRect];
    [button setTitle:@"Move" forState:UIControlStateNormal];
    [button addTarget:self action:@selector(touchDown:) forControlEvents:UIControlEventTouchDown];
    [button addTarget:self action:@selector(touchUp:) forControlEvents:UIControlEventTouchUpInside];
    [button addTarget:self action:@selector(touchUp:) forControlEvents:UIControlEventTouchUpOutside];
    [button sizeToFit];
    button.center = CGPointMake(100, 380);
    button.autoresizingMask = UIViewAutoresizingFlexibleTopMargin | UIViewAutoresizingFlexibleRightMargin;
    [self.view addSubview:button];
}

- (IBAction)touchDown:(id)sender {
    [self animateLayer:_layer toY:kDownY withBaseY:kUpY];
}

- (IBAction)touchUp:(id)sender {
    [self animateLayer:_layer toY:kUpY withBaseY:kDownY];
}

#if 1

- (void)animateLayer:(CALayer *)layer toY:(CGFloat)y withBaseY:(CGFloat)baseY {
    CGPoint fromValue = [layer.presentationLayer position];
    CGPoint toValue = CGPointMake(fromValue.x, y);

    layer.position = toValue;

    CABasicAnimation *animation = [CABasicAnimation animationWithKeyPath:@"position"];
    animation.fromValue = [NSValue valueWithCGPoint:fromValue];
    animation.toValue = [NSValue valueWithCGPoint:toValue];
    animation.duration = 2.0 * (toValue.y - fromValue.y) / (y - baseY);
    [layer addAnimation:animation forKey:animation.keyPath];
}

#else

- (void)animateLayer:(CALayer *)layer toY:(CGFloat)y withBaseY:(CGFloat)baseY {
    CGPoint fromValue = [layer.presentationLayer position];
    CGPoint toValue = CGPointMake(fromValue.x, y);

    layer.position = toValue;

    UIBezierPath *path = [UIBezierPath bezierPath];
    [path moveToPoint:fromValue];
    [path addLineToPoint:toValue];

    CAKeyframeAnimation *animation = [CAKeyframeAnimation animationWithKeyPath:@"position"];
    animation.path = path.CGPath;
    animation.duration =  2.0 * (toValue.y - fromValue.y) / (y - baseY);

    CAAnimationGroup *group = [CAAnimationGroup animation];
    group.duration = animation.duration;
    group.animations = @[animation];
    [layer addAnimation:group forKey:animation.keyPath];
}

#endif

@end